arXiv research

We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. …

By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang…

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plan…

Study finds modular classes help in proving Berezin volumes for supersymmetric theories.

We review the relations between (twisted) supersymmetric gauge theories in four dimensions and moduli problems in four-dimensional topology, and we study in detail the non-abelian monopole equations from this point of view. The relevance of exact results in N=1 and N=2 supersymmetric gauge theories to the computation o…

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of …

We develop a systematic method for classifying supersymmetric orbifold compactifications of M-theory. By restricting our attention to abelian orbifolds with low order, in the special cases where elements do not include coordinate shifts, we construct a "periodic table" of such compactifications, organized according to …

This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.

A new formula connects supersymmetric path integrals to Chern-Simons theory.

Study S-duality and supersymmetry on curved manifolds using localization.

We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for $1|1$-dimensional EFTs from the data of a gerbe with connection.

We show that the maximally supersymmetric pp-waves of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS x S solutions. In addition we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS x S background is either Minkowski space or a maximally…

The paper quantizes hybrid topological-holomorphic field theories on $\mathbb{R}^m imes \mathbb{C}^n$.

We classify (up to local isometry) the maximally supersymmetric solutions of the eleven- and ten-dimensional supergravity theories. We find that the AdS solutions, the Hpp-waves and the flat space solutions exhaust them.

Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is noncompact, constitute a prototype for the formation of singularities, the so-ca…

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then d…

Constructs maps from field theories to complexified K-theory and elliptic cohomology.

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions d…

We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the geometry of backgrounds of key supergravity theories, which have applications in the c…

We present a cocycle model for elliptic cohomology with complex coefficients in which methods from 2-dimensional quantum field theory can be used to rigorously construct cocycles. For example, quantizing a theory of vector bundle-valued fermions yields a cocycle representative of the elliptic Thom class. This construct…

We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an $L^2$ index theorem, we prove the existence of certain BPS stat…

In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss in detail the recent developments in Donaldson-Witten theory obtained from the ap…

Unified treatment of gauge theories and Yang-Mills theory duality.

A class of 3d $\mathcal{N}=2$ supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class…

M-theory preons -- solutions of eleven-dimensional supergravity preserving 31 supersymmetries -- have recently been shown to be locally maximally supersymmetric. This implies that if preons exist they are quotients of maximally supersymmetric solutions. In this paper we show that no such quotients exist. This is achiev…

The paper generalizes Yang-Mills theory to study four-manifold topology.

We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the $SU(2)$ theory on a compact oriented simply connected simple type Riemann manifold with $b_2^+ \geq 3$. As the corollaries,…

We construct supersymmetric field theories on Riemannian three-manifolds M, focusing on N=2 theories with a U(1)_R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet containing the R-current and the energy-momentum tensor. T…

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we emphasize geometric aspects. The beginning chapters give a general discussion about su…

Investigates how adding a scalar potential affects Dirac-harmonic maps.

In this paper we describe multigraded generalizations of some constructions useful for mathematical understanding of gauge theories: we perform a near-at-hand generalization of the Aleksandrov--Kontsevich--Schwarz--Zaboronsky procedure, we also extend the formalism of $Q$-bundles introduced first by A. Kotov and T. Str…

We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in …

We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we…

We classify generalised supersymmetric fluxbranes in type II string theory obtained as Kaluza-Klein reductions of the Minkowski space vacuum of eleven-dimensional supergravity. We obtain two families of smooth solutions which contains all the known solutions, new solutions called nullbranes, and solutions interpolating…

We analyse the most general N=2 supersymmetric solutions of D=11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y_7. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structur…

We show that the baryon number of N=2 supersymmetric QCD can be twisted in order to couple the topological field theory of non-abelian monopoles to $Spin^c$-structures. To motivate the construction, we also consider some aspects of the twisting procedure as a gauging of global currents in two and four dimensions, in pa…

We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of the vortex equations and computes the Hamiltonian Gromov-Witten invariants. When t…

Study torsion parallel spinors on Lorentzian 4-manifolds and their evolution flows.

We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use techniques developed for the classification of supersymmetric solutions to superg…

Geometrically classifies maps from R^0|2 to any manifold, unifying theories.

We construct ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equi…

Constructs BPS complexes and Chern--Simons theories from G-structures.

Discover gaps in q-series exponents for 3d N=2 theories.

In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general for…

In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by …

One has believed that low energy effective theories of the Higgs branch of gauged linear sigma models correspond to supersymmetric nonlinear sigma models, which have been already investigated by many works. In this paper we discuss a explicit derivation of supersymmetric nonlinear sigma models from gauged linear sigma …

The aim of this talk is to explain how symmetry breaking in a quantum field theory problem leads to a study of projective bundles, Dixmier-Douady classes, and associated gerbes. A gerbe manifests itself in different equivalent ways. Besides the cohomological description as a DD class, it can be defined in terms of a fa…

We consider finite deformations of the Hull--Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a third-order Maurer--Cartan equation that controls the moduli. The resulting…