Searcharxiv⌕ Search

arXiv subjects

Martin Roček

Publications and source records attributed to Martin Roček.

11 recordsLinked to original sources
arXiv2026

Ricci-flat metrics from gauged linear $σ$-models without RG flow

We investigate a class of Ricci-flat Kähler metrics on generalized conifolds constructed via gauged linear sigma models (GLSMs) with indefinite signature. By introducing shadow coordinates (superfields) entering the sigma model with negative signature kinetic term, we show that these GLSMs yield explicit Ricci-flat metrics on complex cones over products of projective spaces. We provide a general formula for the resulting Kähler potentials, along with detailed examples. Our results suggest new directions for the study of Calabi-Yau metrics and toric geometry, and raise interesting questions about the geometric meaning of indefinite signature models. We also give an interpretation in terms of a novel generalized Kähler gauging.

hep-th↗
arXiv2026

The Large Vector Multiplet and Gauging $(2,2)$ $σ$-models

The Large Vector Multiple (LVM) is the relevant gauge multiplet for gauging isometries acting on both the chiral and the twisted chiral fields in a $(2, 2)$ sigma model. Here we show that a recently proposed new gauge multiplet is a constrained or partially dualized version of the LVM. Gauging using this multiplet results in a $(2, 2)$ $βγ$ system interacting with a sigma model.

hep-th↗
arXiv2025

Superspace Supergravity

We give a brief, incomplete, and idiosyncratic review of the early years of supergravity in superspace as our contribution to the book Half a Century of Supergravity edited by Anna Ceresole and Gianguido Dall'Agata.

hep-th↗
arXiv2023

Superconformal Gravity And The Topology Of Diffeomorphism Groups

Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a useful point of view on the Donaldson and Seiberg-Witten invariants of four-manifolds. In this paper we generalize the construction to include a path integral formulation of generalizations of Donaldson invariants for smooth families of four-manifolds. Mathematically these are equivariant cohomology classes for the action of the oriented diffeomorphism group on the space of metrics on the manifold. In principle these cohomology classes should contain nontrivial information about the topology of the diffeomorphism group of the four-manifold. We show that the invariants may be interpreted as the standard topologically twisted path integral of four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills coupled to topologically twisted background fields of conformal supergravity.

hep-th↗
arXiv2023

$(0,4)$ Projective Superspaces I: Interacting Linear Sigma Models

We describe the projective superspace approach to supersymmetric models with off-shell $(0,4)$ supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables -- one doublet for each $\text{SU}(2)$ in the R-symmetry $\text{SU}(2) \times \text{SU}(2)$ which are interpreted as homogeneous coordinates on $\mathbf{CP}^1 \times \mathbf{CP}^1$. The superfields are analytic in the $\mathbf{CP}^1$ coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten's ADHM sigma model -- a linear sigma model with non-derivative interactions whose target is $\mathbf{R}^4$ with a Yang-Mills instanton solution. The hyperkähler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction.

hep-th↗
arXiv2019

3D Dualities and Supersymmetry Enhancement from Domain Walls

We test recently proposed IR dualities and supersymmetry enhancement by studying the supersymmetry on domain walls. In the $SU(3)$ Wess-Zumino model studied in arXiv:1804.02018 and arXiv:1804.05707, we show that domain walls exhibit supersymmetry enhancement. This model was conjectured to be dual to an $\mathcal{N}=2$ abelian gauge theory. We show that domain walls on the gauge theory side are consistent with the proposed duality, as they are described by the same effective theory on the wall. In arXiv:1808.04173, a third model was conjectured to be dual to the same IR theory. We study the phases and domain walls of this model and we show that they also agree. We then consider the analogous $SU(5)$ Wess-Zumino model, and study its mass deformations and phases. We argue that even though one might expect supersymmetry enhancement in this model as well, the analysis of its domain walls shows that there is none. Finally, we study the $\mathcal{N}=2$ model in arXiv:1806.07714 which was conjectured to have $\mathcal{N}=4$ supersymmetry in the IR. In this case we don't see the supersymmetry enhancement on the domain wall; however, we argue that half-BPS domain walls of the $\mathcal{N}=2$ algebra are quarter-BPS of the $\mathcal{N}=4$ algebra. This is then in agreement with the conjectured enhancement, even though it does not show that it takes place.

hep-th↗
arXiv2015

On gauged linear sigma models with torsion

We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N=(2,2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chiral, twisted chiral, and semichiral multiplets to known as well as to a new N=(2,2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kahler, hyperkahler, and Calabi-Yau manifolds. The (2,2) supersymmetry guarantees that these spaces are generalized Kahler. Our analysis of the geometric structure is performed at the classical level, but we also discuss quantum aspects such as R-symmetry anomalies. We provide an explicit example of a generalized Kahler structure on the conifold.

hep-th↗
arXiv2012

Generalized Kähler Geometry in (2,1) superspace

Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized Kähler geometry. We investigate the reduction from (2,2) to (2,1) superspace. This has some interesting nontrivial features arising from the elimination of nondynamical fields. We compare quantization in the different superspace formulations.

hep-th↗
arXiv1995

Effective Actions and Gauge Field Stability

By studying an effective action description of the coupling of charged gauge fields in N=2 SU(n) supersymmetric Yang-Mills theories, we can describe regions of moduli space where one or more of these fields becomes unphysical. We discuss subtleties in the structure of the moduli space for SU(3).

hep-th↗
arXiv1994

The Nonlinear Multiplet Revisited

Using a reformulation of the nonlinear multiplet as a gauge multiplet, we discuss its dynamics. We show that the nonlinear ``duality'' that appears to relate the model to a conventional $σ$-model introduces a new sector into the theory.

hep-th↗