arXiv subjects

Daniel Butter

Publications and source records attributed to Daniel Butter.

At least 37 records · Page 2Linked to original sources

arXiv2016

Invariants for minimal conformal supergravity in six dimensions

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 conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric $F \Box F$ invariant in curved superspace.

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arXiv2015

Rigid 4D N=2 supersymmetric backgrounds and actions

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 provide the generic two-derivative rigid vector and hypermultiplet actions and analyze the conditions imposed on the special Kahler and hyperkahler target spaces.

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arXiv2015

Conformal supergravity in five dimensions: New approach and applications

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 superconformal tensor calculus (formulated in the early 2000's) upon gauging away a number of superfluous fields. On the other hand, a different gauge fixing reduces our formulation to the SU(2) superspace of arXiv:0802.3953, which is suitable to describe the most general off-shell supergravity-matter couplings. Using the conformal superspace approach, we show how to reproduce practically all off-shell constructions derived so far, including the supersymmetric extensions of $R^2$ terms, thus demonstrating the power of our formulation. Furthermore, we construct for the first time a supersymmetric completion of the Ricci tensor squared term using the standard Weyl multiplet coupled to an off-shell vector multiplet. In addition, we present several procedures to generate higher-order off-shell invariants in supergravity, including higher-derivative ones. The covariant projective multiplets proposed in arXiv:0802.3953 are lifted to conformal superspace, and a manifestly superconformal action principle is given. We also introduce unconstrained prepotentials for the vector multiplet, the ${\cal{O}}(2)$ multiplet (i.e., the linear multiplet without central charge) and ${\cal{O}}(4+n)$ multiplets, with $n=0,1,\dots$ Superform formulations are given for the BF action and the non-abelian Chern-Simons action. Finally, we describe locally supersymmetric theories with gauged central charge in conformal superspace.

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arXiv2015

Projective multiplets and hyperkahler cones in conformal supergravity

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 corresponding to a generic 4n-dimensional hyperkahler cone. We show how the component action coupling the hypermultiplets to conformal supergravity may be constructed starting from curved superspace. The superspace origin of the geometric data -- the hyperkahler potential, complex structures, and any gauged isometries -- is also addressed.

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arXiv2014

The Anomaly Structure of Regularized Supergravity

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 Kähler moduli $T^i$ obtained from orbifold compactification of the weakly coupled heterotic string. This procedure requires constraints on the chiral matter representations of the gauge group that are consistent with known results from orbifold compactifications. Pauli-Villars regulator fields allow for the cancellation of all quadratic and logarithmic divergences, as well as most linear divergences. If all linear divergences were canceled, the theory would be anomaly free, with noninvariance of the action arising only from Pauli-Villars masses. However there are linear divergences associated with nonrenormalizable gravitino/gaugino interactions that cannot be canceled by PV fields. The resulting chiral anomaly forms a supermultiplet with the corresponding conformal anomaly, provided the ultraviolet cut-off has the appropriate field dependence, in which case total derivative terms, such as Gauss-Bonnet, do not drop out from the effective action. The anomalies can be partially canceled by the four-dimensional version of the Green-Schwarz mechanism, but additional counterterms, and/or a more elaborate set of Pauli-Villars fields and couplings, are needed to cancel the full anomaly, including D-term contributions to the conformal anomaly that are nonlinear in the parameters of the anomalous transformations.

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arXiv2014

A new approach to curved projective superspace

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 to the central gauge where the auxiliary SU(2) manifold largely decouples from the curved manifold M^{4|8} describing 4D N=2 conformal supergravity. We introduce the relevant projective superspace action principle in the analytic subspace of M^{7|8} and construct its component reduction in terms of a five-form J living on M^4 x C, with C a contour in SU(2). This approach is inspired by and generalizes the original approach taken in arXiv:0805.4683 and related works, which can be identified with a complexified version of the central gauge of the formulation presented here.

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arXiv2014

Non-renormalization theorems and N=2 supersymmetric backgrounds

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 and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.

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arXiv2013

New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term

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_{μν}^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 of the square of the Weyl tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.

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arXiv2013

Conformal supergravity in three dimensions: Off-shell actions

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 fields belonging to the Weyl supermultiplet. The N=1 and N=2 component actions derived coincide with those proposed by van Nieuwenhuizen and Rocek in the mid-1980s. The off-shell N=3, N=4 and N=5 supergravity actions are new results. Upon elimination of the auxiliary fields, these actions reduce to those constructed by Lindstrom and Rocek in 1989 (and also by Gates and Nishino in 1993).

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arXiv2013

Nonlocal action for the super-Weyl anomalies: A new representation

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.

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arXiv2013

Conformal supergravity in three dimensions: New off-shell formulation

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 out to be the super Cotton tensor. An immediate corollary of this construction is that the curved superspace is conformally flat if and only if the super Cotton tensor vanishes. Upon degauging of certain local symmetries, our formulation is shown to reduce to the conventional one with the local structure group SL(2,R) x SO(N).

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arXiv2013

Relating harmonic and projective descriptions of N=2 nonlinear sigma models

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 symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.

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arXiv2012

Nonlinear sigma models with AdS supersymmetry in three dimensions

In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative integers p>=q such that p+q=N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target space geometry of supersymmetric nonlinear sigma-models. We classify all possible types of hyperkahler target spaces for the cases N=3 and N=4 by making use of two different realizations for the most general (p,q) supersymmetric sigma-models: (i) off-shell formulations in terms of N=3 and N=4 projective supermultiplets; and (ii) on-shell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N=3,4 AdS supersymmetry, nonlinear sigma-models can support one of the following target space geometries: (i) hyperkahler cones; (ii) non-compact hyperkahler manifolds with a U(1) isometry group which acts non-trivially on the two-sphere of complex structures; (iii) arbitrary hyperkahler manifolds including compact ones. The option (iii) is realized only in the case of critical (4,0) AdS supersymmetry. As an application of the (4,0) AdS techniques developed, we also construct the most general nonlinear sigma-model in Minkowski space with a non-centrally extended N=4 Poincare supersymmetry. Its target space is a hyperkahler cone (which is characteristic of N=4 superconformal sigma-models), but the sigma-model is massive. The Lagrangian includes a positive potential constructed in terms of the homothetic conformal Killing vector the target space is endowed with. This mechanism of mass generation differs from the standard one which corresponds to a sigma-model with the ordinary N=4 Poincare supersymmetry and which makes use of a tri-holomorphic Killing vector.

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arXiv2012

The linear multiplet and ectoplasm

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 construction of supersymmetric invariants). We propose a new locally supersymmetric action which makes use of a deformed linear multiplet. The novel feature of this multiplet is that it corresponds to the case of a gauged central charge using a one-form potential not annihilated by the central charge (unlike the standard N=2 vector multiplet). Such a gauge one-form can be chosen to describe a variant nonlinear vector-tensor multiplet. As a byproduct of our construction, we also find a variant realization of the tensor multiplet in supergravity where one of the auxiliaries is replaced by the field strength of a gauge three-form.

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arXiv2012

Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets

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 multiplets coupled to conformal supergravity are considered directly within projective superspace, where their formulation is most natural. We then demonstrate how the inverse procedure -- the lifting of component results to superspace -- can simplify the analysis of complicated multiplets. We address the off-shell N=2 vector-tensor multiplet coupled to conformal supergravity with a central charge and demonstrate explicitly how its constraints and Lagrangian can be written in a simpler way using superfields.

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arXiv2012

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.

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arXiv2012

New higher-derivative couplings in 4D N = 2 supergravity

Using the off-shell formulation for general 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 L. One can choose L to be composed of tensor multiplets, O(2n) multiplets, with n=2,3,..., and polar hypermultiplets. In conjunction with the standard procedure to induce a N = 2 linear multiplet from any chiral weight-one scalar, we obtain a powerful mechanism to generate higher-derivative couplings in supergravity. In the case that L is a homogeneous function of n tensor multiplets of degree zero, we show that our construction is equivalent to that developed by de Wit and Saueressig in arXiv:hep-th/0606148 using the component superconformal tensor calculus. We also work out nontrivial examples with L composed of O(2n)and tensor multiplets.

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arXiv2012

Generating higher-derivative couplings in N=2 supergravity

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 integral over 3/4 of the Grassmann coordinates of superspace.

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