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Martin Rocek

Publications and source records attributed to Martin Rocek.

At least 19 recordsLinked to original sources
arXiv2022

Pure Supersymmetric AdS and the Swampland

We point out that pure supergravity theories in $AdS$ with enough supersymmetry lead, upon taking the large radius limit, to flat space quantum gravities with a nonperturbatively exact global symmetry, and are therefore in the Swampland. The argument applies to any $AdS$ supergravity with gauged R-symmetry group, including truncations of most well known examples, such as $AdS_5$ without the $S^5$ or $AdS_4$ without the $S^7$. This demonstrates that extreme scale separation, at least with enough supersymmetry, is not realizable. Moreover pure $AdS$ theories are also in conflict with some other Swampland principles including the Weak Gravity Conjecture and the (generalized) Distance Conjecture.

hep-th↗
arXiv2019

Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions

We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding $A_{\infty}$-structures. In $N=2$ 3D space we construct the homotopic counterpart of the de Rham complex, which is related to the superfield formulation of the $N=2$ Chern-Simons theory.

math-ph↗
arXiv2018

Dualities and Phases of 3D N=1 SQCD

We study gauge theories with N=1 supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter. Using the 1-loop superpotential, we find a universal form for the phase diagrams of many such gauge theories, which is proven to persist to all orders in perturbation theory using a symmetry argument. This allows us to conjecture new dualities for N=1 gauge theories with fundamental matter. We also show that these dualities are related to results in N=2 supersymmetric gauge theories, which provides further evidence for them.

hep-th↗
arXiv2018

Generalized Kahler structures on group manifolds and T-duality

We study generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models; we use the well known case of SU(2) x U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the highly nontrivial structure of the hitherto unexplored case of SU(3); these tools should be useful for studying many other examples. We find that different generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models can be found by T-duality transformations along affine isometries.

hep-th↗
arXiv2016

Kahler-Einstein and Kahler scalar flat supermanifolds

Two results regarding Kähler supermanifolds with potential $K=A+Cθ\barθ$ are shown. First, if the supermanifold is Kähler-Einstein, then its base (the supermanifold of one lower fermionic dimension and with Kähler potential $A$) has constant scalar curvature. As a corollary, every constant scalar curvature Kähler supermanifold has a unique superextension to a Kähler-Einstein supermanifold of one higher fermionic dimension. Second, if the supermanifold is itself scalar flat, then its base satisfies the equation $$ ϕ^{\bar ji}ϕ_{i\bar j}=2Δ_0 S_0 + R_0^{\bar ji}R_{0i\bar j} - S_0^2, $$ where $Δ_0$ is the Laplace operator, $S_0$ is the scalar curvature, and $R_{0i\bar j}$ is the Ricci tensor of the base, and $ϕ$ is some harmonic section on the base. Remarkably, precisely this equation arises in the construction of certain supergravity compactifications. Examples of bosonic manifolds satisfying the equation above are discussed.

hep-th↗
arXiv2014

Three-dimensional N=2 supergravity theories: From superspace to components

For general off-shell N=2 supergravity-matter systems in three spacetime dimensions, a formalism is developed to reduce the corresponding actions from superspace to components. The component actions are explicitly computed in the cases of Type I and Type II minimal supergravity formulations. We describe the models for topologically massive supergravity which correspond to all the known off-shell formulations for three-dimensional N=2 supergravity. We also present a universal setting to construct supersymmetric backgrounds associated with these off-shell supergravities.

hep-th↗
arXiv2012

Semichiral Sigma Models with 4D Hyperkaehler Geometry

Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such models and find that a rather general ansatz for the additional supersymmetry (not involving central charge transformations) leads to hyperkähler geometry. We give non-trivial examples of these models.

hep-th↗
arXiv2011

Does Smoothing Matter?

We study how inhomogeneities modify large scale parameters in General Relativity. For a particular model, we obtain exact results: we compare an infinite string of extremal black holes to a corresponding smooth line with the same mass and charge in five dimensions. We find that the effective energy density does not differ significantly.

gr-qc↗
arXiv2010

Generalized Calabi-Yau metric and Generalized Monge-Ampere equation

In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true. This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.

hep-th↗
arXiv2008

Nonabelian Generalized Gauge Multiplets

We give the nonabelian extension of the newly discovered N = (2, 2) two-dimensional vector multiplets. These can be used to gauge symmetries of sigma models on generalized Kahler geometries. Starting from the transformation rule for the nonabelian case we find covariant derivatives and gauge covariant field-strengths and write their actions in N = (2, 2) and N = (1, 1) superspace.

hep-th↗
arXiv2008

T-duality and Generalized Kahler Geometry

We use newly discovered N = (2, 2) vector multiplets to clarify T-dualities for generalized Kahler geometries. Following the usual procedure, we gauge isometries of nonlinear sigma-models and introduce Lagrange multipliers that constrain the field-strengths of the gauge fields to vanish. Integrating out the Lagrange multipliers leads to the original action, whereas integrating out the vector multiplets gives the dual action. The description is given both in N = (2, 2) and N = (1, 1) superspace.

hep-th↗
arXiv2007

New N = (2, 2) vector multiplets

We introduce two new N = (2, 2) vector multiplets that couple naturally to generalized Kahler geometries. We describe their kinetic actions as well as their matter couplings both in N = (2, 2) and N = (1, 1) superspace.

hep-th↗
arXiv2007

A potential for Generalized Kahler Geometry

We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an auxiliary local product (ALP) space.

hep-th↗
arXiv2007

Linearizing Generalized Kahler Geometry

The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlinear functions of the second derivatives of K. We show that, at least locally, the nonlinearity on any generalized Kahler manifold can be explained as arising from a quotient of a space without this nonlinearity.

hep-th↗
arXiv2007

Orientifolding in N=2 Superspace

We discuss orientifold projections on superspace effective actions for hypermultiplets. We present a simple and new mechanism that allows one to find the Kahler potential and complex structure for the N=1 theory directly in terms of the parent N=2 theory. As an application, we demonstrate our method for Calabi-Yau orientifold compactifications of type IIB superstrings.

hep-th↗
arXiv2006

SIM(2) and Superspace

In this brief note we give a superspace description of the supersymmetric nonlocal Lorentz noninvariant actions recently proposed by Cohen and Freedman. This leads us to discover similar terms for gauge fields.

hep-th↗