Daniel Butter's research while affiliated with Texas A&M University and other places
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Publications (68)
Using a recently developed formulation of double field theory in superspace, the graviton, B-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic O(D, D) duality group, and these act on all constituents...
Using a recently developed formulation of double field theory in superspace, the graviton, $B$-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic $O(D,D)$ duality group, and these act on all constituen...
A bstract
The Ramond-Ramond sector of double field theory (DFT) can be described either as an O( D, D ) spinor or an O( D − 1 , 1) × O(1 , D − 1) bispinor. Both formulations may be related to the standard polyform expansion in terms of even or odd rank field strengths corresponding to IIA or IIB duality frames. The spinor approach is natural in a (...
A bstract
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality....
A bstract
We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group OSp(10 , 10|64), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic double field theory, the local tangent space must be enhanced from the double Lorentz group in order...
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we d...
A bstract
We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, G 2 -structure which facilitates the definition of a 4|4 + 7 background superspace. A bottom-up construction of...
We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group OSp(10,10|64), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic double field theory, the local tangent space must be enhanced from the double Lorentz group in order to eliminate...
The Ramond-Ramond sector of double field theory (DFT) can be described either as an O(D,D) spinor or an O(D-1,1) x O(1,D-1) bispinor. Both formulations may be related to the standard polyform expansion in terms of even or odd rank field strengths corresponding to IIA or IIB duality frames. The spinor approach is natural in a (bosonic) metric formul...
We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, $G_2$-structure which facilitates the definition of a $4|4+7$ background superspace. A bottom-up construction of linear f...
A bstract
The geometry of $$ \mathcal{N} $$ N = 1 supersymmetric double field theory is revisited in superspace. In order to maintain the constraints on the torsion tensor, the local tangent space group of O( D ) × O( D ) must be expanded to include a tower of higher dimension generators. These include a generator in the irreducible hook representa...
A bstract
We derive the component structure of 11D, N = 1/8 supergravity linearized around eleven-dimensional Minkowski space. This theory represents 4 local supersymmetries closing onto 4 of the 11 spacetime translations without the use of equations of motion. It may be interpreted as adding 201 auxiliary bosons and 56 auxiliary fermions to the ph...
We derive the component structure of 11D, $N=1/8$ supergravity linearized around eleven-dimensional Minkowski space. This theory represents 4 local supersymmetries closing onto 4 of the 11 spacetime translations without the use of equations of motion. It may be interpreted as adding $201$ auxiliary bosons and $56$ auxiliary fermions to the physical...
The geometry of N=1 supersymmetric double field theory is revisited in superspace. In order to maintain the constraints on the torsion tensor, the local tangent space group of O(D) x O(D) must be expanded to include a tower of higher dimension generators. These include a generator in the irreducible hook representation of the Lorentz group, which g...
A bstract
Motivated by recent efforts to encode 11D supergravity in 4D $$ \mathcal{N} $$ N = 1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D $$ \mathcal{N} $$ N = 1 superspace with n additional internal coordinates. The superspace geometry admits both extern...
Motivated by recent efforts to encode 11D supergravity in 4D N=1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D N=1 superspace with n additional internal coordinates. The superspace geometry admits both external and internal diffeomorphisms and provides the s...
A bstract
We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincaré symmetries manifestly. The remaining four supersymmetries and the rest of the Poincaré symmetries are represented linearly but not manifestly. In the linearized approximati...
The most general class of 4D \( \mathcal{N} \) = 4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1, 1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [1]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new \( \...
The most general class of 4D N=4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1,1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [arXiv:1609.09083]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new N=4 dens...
We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincar\'e symmetries manifestly. The remaining four supersymmetries and the rest of the Poincar\'e symmetries are represented linearly but not manifestly. In the linearized approximation, th...
A bstract
We describe the supersymmetric completion of several curvature-squared invariants for $$ \mathcal{N} $$ N = (1, 0) supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matt...
A bstract
We formulate the locally supersymmetric E 7(7) exceptional field theory in a (4 + 56|32) dimensional superspace, corresponding to a 4D N = 8 “external” superspace augmented with an “internal” 56-dimensional space. This entails the unification of external diffeomorphisms and local supersymmetry transformations into superdiffeomorphisms. Th...
We formulate the locally supersymmetric E$_{7(7)}$ exceptional field theory in a $(4+56|32)$ dimensional superspace, corresponding to a 4D $N\!=\!8$ "external" superspace augmented with an "internal" 56-dimensional space. This entails the unification of external diffeomorphisms and local supersymmetry transformations into superdiffeomorphisms. The...
We describe the supersymmetric completion of several curvature-squared invariants for ${\cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the c...
A bstract
Eleven-dimensional supergravity can be formulated in superspaces locally of the form X × Y where X is 4D N = 1 conformal superspace and Y is an arbitrary 7-manifold admitting a G 2 -structure. The eleven-dimensional 3-form and the stable 3-form on Y define the lowest component of a gauge superfield on X × Y that is chiral as a superfield...
A bstract
We construct the dilaton Weyl multiplet for N = 2 conformal supergravity in four dimensions. Beginning from an on-shell vector multiplet coupled to the standard Weyl multiplet, the equations of motion can be used to eliminate the supergravity auxiliary fields, following a similar pattern as in five and six dimensions. The resulting 24+24...
A bstract
We give a formulation of linearized 11D supergravity in 4D, N = 1 superspace keeping all eleven bosonic coordinates. The fields are fluctuations around M = R 4|4 × Y , where Y is a background Riemannian 7-manifold admitting a G 2 structure. We embed the 11D fields into superfield representations of the 4D, N = 1 superconformal algebra. Th...
All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this func...
In the recent paper arXiv:1606.02921, the two invariant actions for 6D $N=(1,0)$ conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of $C^3$ and $C\Box C$. In this paper, we provide the translation from superspace to the component formulation of superconformal tensor calculus, and we give the full compon...
All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this func...
We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D ${\cal N} = (1, 0)$ superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D ${\cal N} = (1, 0)$ conformal supergravity, which contain $C^3$ and $C\Box C$ terms at the component level. Using a con...
This paper describes a fully covariant approach to harmonic superspace. It is
based on the conformal superspace description of conformal supergravity and
involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The
resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with
the conventional harmonic superspace...
Projective superspace provides a natural framework for the construction of actions coupling hypermultiplets to conformal supergravity. We review how the off-shell actions are formulated in superspace and then discuss how to eliminate the infinite number of auxiliary fields to produce an on-shell N=2$$ \mathcal{N}=2 $$ supersymmetric sigma model, wi...
We classify all N=2 rigid supersymmetric backgrounds in four dimensions with
both Lorentzian and Euclidean signature that preserve eight real supercharges,
up to discrete identifications. Among the backgrounds we find specific warpings
of S^3 x R and AdS_3 x R, AdS_2 x S^2 and H^2 x S^2 with generic radii, and
some more exotic geometries. We provid...
In a recent paper [1], we constructed a novel class of higher derivative invariants in 4DN = 2 supergravity that included, as a special case, the supersymmetric Gauss-Bonnet invariant. Here we give a brief description of these results and highlight the potential applications.
We briefly review the novel off-shell formulation for \(\mathcal{N}\)-extended conformal supergravity in three spacetime dimensions developed in [1]. Our approach is based on gauging the \(\mathcal{N}\)-extended superconformal algebra \(\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {\left. \mathcal{N} \right|4,\mathbb{R}} \right)\) in superspace. A sp...
We review the recent construction of the N ≤ 6 off-shell conformal supergravity actions in three dimensions. The approach makes use use of a novel superspace formulation for N-extended conformal supergravity and the superform approach to engineer supersymmetric invariants.
We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the super-conformal tensor calculus (formulated in the early 2000’s) upon gauging away a number of superfluous fie...
On-shell Pauli-Villars regularization of the one-loop divergences of
supergravity theories is used to study the anomaly structure of supergravity
and the cancellation of field theory anomalies under a $U(1)$ gauge
transformation and under the T-duality group of modular transformations in
effective supergravity theories with three K\"ahler moduli $T...
Projective superspace provides a natural framework for the construction of
actions coupling hypermultiplets to conformal supergravity. We review how the
off-shell actions are formulated in superspace and then discuss how to
eliminate the infinite number of auxiliary fields to produce an on-shell N=2
supersymmetric sigma model, with the target space...
We present a new formulation of curved projective superspace. The 4D N=2
supermanifold M^{4|8} (four bosonic and eight Grassmann coordinates) is
extended by an auxiliary SU(2) manifold, which involves introducing a vielbein
and related connections on the full M^{7|8} = M^{4|8} x SU(2). Constraints are
chosen so that it is always possible to return...
The conditions for fully supersymmetric backgrounds of general N=2 locally
supersymmetric theories are derived based on the off-shell superconformal
multiplet calculus. This enables the derivation of a non-renormalization
theorem for a large class of supersymmetric invariants with higher-derivative
couplings. The theorem implies that the invariant...
A new class of N=2 locally supersymmetric higher-derivative invariants is
constructed based on logarithms of conformal primary chiral superfields. They
characteristically involve a coupling to R_{\mu\nu}^2 - 1/3*R^2, which equals
the non-conformal part of the Gauss-Bonnet term. Upon combining one such
invariant with the known supersymmetric version...
Using the recently discovered N=1 supersymmetric extension of the conformal
fourth-order scalar operator (introduced originally by Fradkin and Tseytlin and
also known as the "Paneitz operator" or "Riegert operator"), we derive a new
representation for the nonlocal action generating the super-Weyl anomalies.
Using the off-shell formulation for N-extended conformal supergravity in
three dimensions, which has recently been presented in arXiv:1305.3132, we
construct superspace actions for conformal supergravity theories with N<6. For
each of the cases considered, we work out the complete component action as well
as the gauge transformation laws of the fie...
We propose a new off-shell formulation for N-extended conformal supergravity
in three spacetime dimensions. Our construction is based on the gauging of the
N-extended superconformal algebra in superspace. Covariant constraints are
imposed such that the algebra of covariant derivatives is given in terms of a
single curvature superfield which turns o...
In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of \( \mathcal{N} \) -extended supersymmetry, which are traditionally labelled by two non-negative integers p ≥ q such that p + q = \( \mathcal{N} \). Different choices of p and q, with \( \mathcal{N} \) fixed, prove to lead to different restrictions on the target spa...
Using a recently developed off-shell formulation for general 4D N=2
supergravity-matter systems, we propose a construction to generate higher
derivative couplings. We address here mainly the interactions of tensor and
vector multiplets, but the construction is quite general. For a certain
subclass of terms, the action is naturally written as an int...
Recent papers have established the relationship between projective superspace
and a complexified version of harmonic superspace. We extend this construction
to the case of general nonlinear sigma models in both frameworks. Using an
analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian
structure of the harmonic action and the symple...
In the framework of the superconformal tensor calculus for 4D N=2
supergravity, locally supersymmetric actions are often constructed using the
linear multiplet. We provide a superform formulation for the linear multiplet
and derive the corresponding action functional using the ectoplasm method (also
known as the superform approach to the constructi...
There exist two superspace approaches to describe \( \mathcal{N} = 2 \) supersymmetric nonlinear σ-models in four-dimensional anti-de Sitter (AdS4) space: (i) in terms of \( \mathcal{N} = 1 \) AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of \( \mathcal{N} = 2 \) polar supermultiplets using the AdS p...
Recent advances in curved N=2 superspace methods have rendered the component
reduction of superspace actions more feasible than in the past. In this paper,
we consider models involving both vector and tensor multiplets coupled to
supergravity and demonstrate explicitly how component actions may be
efficiently obtained. In addition, tensor multiplet...
We present a detailed study of the most general
$ \mathcal{N} = {2} $
supersymmetric sigma models in four-dimensional anti-de Sitter space (AdS4) formulated in terms of
$ \mathcal{N} = 1 $
chiral superfields. The target space is demonstrated to be a non-compact hyperkähler manifold restricted to possess a special Killing vector field which gene...
We present a detailed study of the most general N=2 supersymmetric sigma
models in four-dimensional anti-de Sitter space AdS_4 formulated in terms of
N=1 chiral superfields. The target space is demonstrated to be a non-compact
hyperkahler manifold restricted to possess a special Killing vector field which
generates an SO(2) group of rotations on th...
Generating supersymmetric AdS solutions in non-minimal supergravity in four
dimensions is notoriously difficult. Indeed, it is a longstanding lore that
such solutions exist only for old minimal supergravity. In this paper, we
construct a dual formulation for general N=1 supergravity-matter systems that
avoids the problem. In the case of pure superg...
We construct the most general N=2 supersymmetric nonlinear sigma-model in
four-dimensional anti-de Sitter (AdS) space in terms of N=1 chiral superfields.
The target space is shown to be a non-compact hyperkahler manifold restricted
to possess a special Killing vector field. A remarkable property of the
sigma-model constructed is that the algebra of...
We consider the minimal off-shell formulation for four-dimensional
$ \mathcal{N} = 2 $
supergravity with a cosmological term, in which the second compensator is an improved tensormultiplet. We use it to derive a linearized supergravity action (and its dual versions) around the anti-de Sitter (AdS) background in terms of three
$ \mathcal{N} = 2 $...
We develop the geometry of four dimensional N=2 superspace where the entire
conformal algebra of SU(2,2|2) is realized linearly in the structure group
rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries,
extending to N=2 our prior result for N=1 superspace. This formulation
explicitly lifts to superspace the existing methods...
Using the off-shell formulation for general
$ \mathcal{N} = 2 $
supergravity-matter systems developed in arXiv:0905.0063, we propose a construction to generate a restricted chiral superfield from any real weight-zero projective multiplet
$ \mathcal{L} $
. One can choose
$ \mathcal{O}\left( {2n} \right) $
to be composed of tensor multiplets,
$ \...
We address the problem of classifying all N = 2 \mathcal{N} = 2 supercurrent multiplets in four space-time dimensions. For this purpose we consider the minimal formulation of N = 2 \mathcal{N} = 2 Poincaré supergravity with a tensor compensator, and derive its linearized action in terms of three N = 2 \mathcal{N} = 2 off-shell multiplets: an uncons...
Recently there has appeared in the literature a sequence of papers questioning the consistency of supergravity coupled to Fayet-Iliopoulos terms. A key feature of these arguments is a demonstration that the conventional superspace stress tensor fails to be gauge invariant. We briefly show here how this can be understood as defining the stress tenso...
We apply the heat kernel method (using Avramidi's non-recursive technique) to the study of the effective action of chiral matter in a complex representation of an arbitrary gauge sector coupled to background U(1) supergravity. This generalizes previous methods, which restricted to 1) real representations of the gauge sector in traditional Poincar\'...
We expand the generic model involving chiral matter, super Yang-Mills gauge fields, and supergravity to second order in the gravity and gauge prepotentials in a manifestly covariant and conformal way. Such a class of models includes conventional chiral matter coupled to supergravity via a conformal compensator. This is a first step toward calculati...
We construct in detail an N=1, D=4 superspace with the superconformal algebra as the structure group and discuss its relation to prior component approaches and the existing Poincar\'e superspaces. Comment: 68 pages, revised introduction
We display the full anomaly structure of supergravity, including new D-term contributions to the conformal anomaly. This expression has the super-Weyl and chiral U(1)_K transformation properties that are required for implementation of the Green-Schwarz mechanism for anomaly cancellation. We outline the procedure for full anomaly cancellation. Our r...
When supersymmetry is broken by condensates with a single condensing gauge group, there is a nonanomalous R-symmetry that prevents the universal axion from acquiring a mass. It has been argued that, in the context of supergravity, higher dimension operators will break this symmetry and may generate an axion mass too large to allow the identificatio...
We present a detailed study of the most general N = 2 supersymmetric sigma models in four-dimensional anti-de Sitter space (AdS 4) formulated in terms of N = 1 chiral superfields. The target space is demonstrated to be a non-compact hyperkähler manifold restricted to possess a special Killing vector field which generates an SO(2) group of rotations...
Citations
... The idea of extending the Abelian dualisation procedure to the case of backgrounds enjoying commuting superisometries was introduced in [46,47] and further developed in [48][49][50][51][52][53][54] -see also [55] for previous related work and [56] for a review. In recent years, it has led to various non-Abelian generalisations, formulated in terms of BRST techniques [57], super Poisson-Lie symmetry [58][59][60][61][62][63][64][65], Double Field Theory formalism [66][67][68][69], as well as manifestly supersymmetric generalizations of the NATD technique of de la Ossa and Quevedo [70][71][72][73][74][75][76], ...
Reference: JT gravity from non-Abelian T-duality
... However, in supergravity this is more subtle because chiral fermions are present, breaking each Lorentz group to its connected (proper orthochronous) component. This means that Λ falls into one of four classes, depending on whether it preserves or reverses the temporal and spatial orientations: this distinguishes the type IIA/IIB/IIA * /IIB * duality frames [36,37,73]. Double field theory conveniently packages the O(D, D) structure of T-duality transformations. ...
Reference: Generalized Dualities and Supergroups
... of the frame. Its splitting is inspired by results for the duality group Oðd; dÞ [11] and will be motivated in the following. Finally, we need the generalized Lie derivative [12] ...
... The Ramond-Ramond sector is particularly onerous, since unlike the other bosonic fields, it does not appear explicitly in the Green-Schwarz σ-model action. 2 The goal of this paper is to address some of these topics from the perspective of a manifestly supersymmetric and duality covariant formulation. Such a formulation has recently been constructed by one of us in the language of double superspace [38], building off earlier work on the subject [26,[39][40][41][42]. Double superspace can be understood in a nutshell as simultaneously geometrizing supersymmetry and T-duality. In conventional superspace, the graviton (vielbein) and gravitino are unified into a single supervielbein, which in a certain gauge reads ...
Reference: Generalized Dualities and Supergroups
... The last two equations contain only fields restricted to M d and thereby do not depend on the additional coordinates of M p introduced by G S . A frame of a similar form was first introduced in [15] for Oðd; dÞ and later further refined to arbitrary structure groups [16]. Therefore, we refer to it as the exceptional Poláček-Siegel form. ...
... One common approach is to take advantage of the manifest symmetries to constrain the higher-derivative terms. This includes making use of supersymmetry [1][2][3][4][5][6][7][8][9][10], S-duality [11][12][13], and, what is relevant to this work, T-duality. T-duality appears when compactifying on a circle, or more generally some d-dimensional torus. ...
... A key missing feature is the additional gravitini supermultiplets, and taking these into account was shown in [10] to correctly reproduce the bosonic part of the linearized component theory. A first step towards its non-linear completion was taken in [11] and the appropriate framework for this eventual completion was constructed in [12]. ...
... To check that such an approach is feasible, we have carried out the analogous calculation in a five-dimensional version of this scenario in [37]. There the invariant is of the JHEP07(2021)032 form A ∧ R 2 where A is the gravi-photon. ...
... in [3]. The cancellation of anomalies was shown also directly in [15]. 2 More recently Tseytlin pointed out [16] that analogous conclusions hold for the non-minimal N = 4 conformal supergravities classified in [4,5]. ...
![[object Object]](https://i1.rgstatic.net/ii/profile.image/279351380725761-1443613967118_Q64/Bindusar-Sahoo.jpg)
... This goes by the name of conformal superspace, which was first introduced by Daniel Butter for 4D, N = 1 supergravity [5] and later extended to different space-time dimensions and amount of supersymmetries -we refer the reader to the following references [27,26] for pedagogical reviews and a complete list of references. In the last decade, this approach has allowed to obtain many new results pushing forward a systematic analysis of higher-derivative supergravity by using off-shell techniques, as exemplified in the results in the following incomplete list of papers [7,8,12,9,25,6,11,29,10,19,17,18,13]. ...
![[object Object]](https://i1.rgstatic.net/ii/profile.image/709663309983745-1546208326807_Q64/Mehmet-Ozkan.jpg)
![[object Object]](https://i1.rgstatic.net/ii/profile.image/783492338167810-1563810538373_Q64/Gabriele-Tartaglino-Mazzucchelli.jpg)
