New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
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Reformulated sigma models for complex Grassmannians using Gross-Neveu formalism.
problem Classical aspects of supersymmetric sigma models with Hermitian symmetric target spaces.
method Reformulation using Gross-Neveu formalism, proposing two types of equivalent Lagrangians.
result Proposed two types of equivalent Lagrangians for maximal isotropic Grassmannians, making either supersymmetry or geometry manifest.
Study of supersymmetric deformations and monopoles in Kahler geometry.
problem Deformation of N = 4 quantum mechanics with Kahler target space.
method Use of matrix-valued functions of the moment map obeying Nahm equations.
result Berry connection on vacuum bundle satisfies BPS monopole equations.
This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.
problem Exploring new maximally supersymmetric backgrounds in five dimensions.
method Classifying Kaluza-Klein reductions to four dimensions and determining preserved supersymmetry.
result Discovery of novel non-homogeneous four-dimensional Lorentzian spacetimes with supersymmetry.
Study finite deformations from heterotic superpotential, leading to new complex effective action.
problem Finite deformations of the Hull--Strominger system.
method Expanding the heterotic superpotential around a supersymmetric vacuum, identifying complex coordinates, and using Maurer--Cartan equation.
result Generalizes complex effective action of Kodaira--Spencer and holomorphic Chern--Simons theory, with a supersymmetric locus described by an algebra.
This paper classifies Killing superalgebras for Lorentzian 4-manifolds.
problem Understanding Killing superalgebras in Lorentzian 4-manifolds.
method Reinterpreting as filtered deformations of subalgebras, computing Spencer cohomology, identifying Killing spinors.
result Maximally supersymmetric backgrounds are classified based on their Killing superalgebras.
Study the algebraic structure of Killing superalgebras in 11D supergravity.
problem Classify highly supersymmetric backgrounds.
method Mapped classification problem to filtered deformations of graded subalgebras of Poincaré superalgebra.
result Reconstructing backgrounds from Killing superalgebras and relating to field equations.
Unified treatment of gauge theories and Yang-Mills theory duality.
problem Unified treatment of gauge theories and Yang-Mills theory duality.
method Cohomological localization techniques and Atiyah-Singer index theorem.
result Unified framework and simplified derivations of localization formulas.
We study massless deformations of generalized calibrated cycles, which describe, in the language of generalized complex geometry, supersymmetric D-branes in N=1 supersymmetric compactifications with fluxes. We find that the deformations are classified by the first cohomology group of a Lie algebroid canonically associa…
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…
The study explores highly supersymmetric backgrounds in 11D supergravity.
problem Understanding and constructing highly supersymmetric backgrounds in 11D supergravity.
method Definition of abstract symbols and a strong version of the Reconstruction Theorem, proposing a strategy to construct backgrounds, and providing an example with detailed computation.
result Bijective correspondence between highly supersymmetric backgrounds and abstract symbols, and a classical supersymmetry gap result.
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are t…
Defines Killing (super)algebras for spin manifolds, including gauge transformations.
problem Understanding deformations of spin structures on manifolds.
method Introduces a new algebraic structure, studies its deformations using Spencer cohomology.
result Identifies subclasses of deformations and reconstructs supersymmetric backgrounds.
The paper classifies supersymmetric backgrounds in 11D gravity.
problem Classifying maximally supersymmetric backgrounds in 11D supergravity.
method Lie algebraic classification of subalgebras of the Poincaré superalgebra.
result There are only three other Lie superalgebras that are symmetry superalgebras of non-flat maximally supersymmetric backgrounds.
Proves super-version of index theorem from algebraic cobordism invariants.
problem Cobordism invariants in supersymmetric quantum mechanics.
method Trace methods for deformation quantization.
result Recovery of cobordism invariant using trace methods.
New cohomology for deformed Sasaki-Einstein manifolds derived from Dolbeault cohomology.
problem Developing a new cohomology structure for deformed Sasaki-Einstein manifolds.
method Introducing -cohomology defined by a CR structure and a holomorphic function with non-vanishing .
result Established a direct relation between the cyclic homologies of the Calabi-Yau algebra and the -cohomology groups.
We find a worldsheet realization of generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. The two-dimensional model we construct is a supersymmetric relative of the Poisson sigma model used in context of deformation quantization.
Geometrically constructs solutions to 11D supergravity.
problem Finding supersymmetric solutions to 11D supergravity.
method Warped product manifolds with non-vanishing flux.
result Explicit 5-parameter moduli space of solutions.
Solutions of tt*-equation from SU(2)_k fusion algebra.
problem Describe solutions to the tt*-equation from a specific algebra.
method Use DPW method and representations of SU(2).
result Construct solutions corresponding to A_k minimal model.
We study some aspects of spherical symmetric dyonic non-supersymmetric black holes in supergravity coupled to chiral and vector multiplets on Kähler-Ricci solitons. Then, we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler-Ricci soliton…
Expanding on supersymmetric Yang-Mills theory, this work focuses on cohomological field theory aspects.
problem Exploring the mathematical aspects of supersymmetric Yang-Mills theory on 4D manifolds.
method Constructing a cohomological field theory using the Atiyah-Jeffrey construction and demonstrating the transversally elliptic complex.
result The deformation theory of flipping instantons is controlled by a transversally elliptic complex, crucial for non-degeneracy and calculability.
We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the transformation relates supersymmetric A- and B-cycles. In this paper, we assume that th…
We identify a deformation of the N=2 supersymmetric sigma model on a Calabi-Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the non…
The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite …
We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions in supersymmetric (SUSY) U(N_C) gauge theories in five dimensions with N_F hypermultiplets in the fundamental representation for infinite gauge coupling. The moduli space of these non-Abelian walls is found…
We consider some aspects of the curved BPS domain walls and their supersymmetric Lorentz invariant vacua of the four dimensional N=1 supergravity coupled to a chiral multiplet. In particular, the scalar manifold can be viewed as a two dimensional Kähler-Ricci soliton generating a one-parameter family of Kähler manifold…
Defines Killing spinors and bosonic backgrounds in 5D supergravity.
problem Characterizing backgrounds in 5D supergravity.
method Calculates Spencer cohomology, defines Killing spinors, and imposes constraints on spinor connection curvature.
result Recover field equations of 5D supergravity and find new field equations for -valued one-form.
We explore the nonperturbative aspects of the chiral algebras of N = (0,2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero. This has some nont…
Study of exceptional algebroids in type IIA string theory.
problem Understanding the structure of algebroids in type IIA string theory.
method Warped compactifications and analysis of local moduli space.
result Local classification of algebroids reveals new scalar deformations and twists.
The paper classifies supersymmetric backgrounds and defines Yang-Mills theory on them.
problem Classifying and defining Yang-Mills theory on supersymmetric backgrounds.
method Classification of maximally supersymmetric backgrounds, determination of conformal symmetry superalgebras, definition of Yang-Mills theory.
result Yang-Mills theory can be defined on supersymmetric conformal supergravity backgrounds.
The paper proves rigidity results for certain supergravity backgrounds in 11 dimensions.
problem Supersymmetry gap problem for supergravity backgrounds in 11 dimensions.
method Study of curvature restrictions and use of bijective correspondence between filtered deformations of Lie superalgebras and highly supersymmetric backgrounds.
result Rigidity results for specific supergravity backgrounds with low rank 4-form and high Killing spinor dimension.
Study of harmonic oscillators on singular geometries using supersymmetry.
problem Global invariants on singular spaces.
method Supersymmetric localization, equivariant localization, Morse theory, geometric quantization.
result Renormalized Lefschetz numbers and Morse polynomials for singular spaces.
Nonreversible Gauge Fields in Fokker--Planck Dynamics: Supersymmetric Hamiltonians and Learned Finite Forcescond-mat.dis-nn
New gauge fields modify Fokker-Planck dynamics without changing the stationary state.
problem Understanding and modifying nonreversible dynamics in Fokker-Planck models.
method Formulate nonreversible perturbations as gauge fields, mapping to supersymmetric Hamiltonians, and learning finite forces.
result Learned finite forces can recover the optimal Lyapunov-equation solution in nonconvex landscapes.
We obtain all possible solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation exactly, containing configurations made of walls, vortices and monopoles in the Higgs phase. We use supersymmetric U(N_C) gauge theories with eight supercharges with N_F fundamental hypermultiplets in the strong coupling limit. The moduli…
Survey on rigorous construction of supersymmetric path integral.
problem Rigorous construction of supersymmetric path integral.
method Construction based on joint work with collaborators.
result Rigorous construction of supersymmetric path integral.
Study of exceptional algebroids in relation to type IIB superstrings.
problem Understanding the structure of exceptional algebroids in type IIB superstring theory.
method Analyzing the local form of IIB-exact exceptional algebroids and deriving possible twists.
result A simple description of Leibniz parallelisable spaces and U-duality.
The paper defines a moduli space for heterotic G2 systems.
problem Deformations of heterotic string compactifications on G2 manifolds.
method Defines a covariant exterior derivative and shows it is equivalent to a heterotic G2 system.
result Determines the infinitesimal moduli space of heterotic G2 systems.
Study of defects in gauge theories connects quantum field theory to classical integrability.
problem Vacuum expectation values of half-BPS surface defects in gauge theories.
method Analysis of Fuchsian systems, isomonodromic deformations, and blowup formulas.
result Establishes a relation between supersymmetric gauge theory and classical integrability.
This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an impor…
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. …
We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that the fluxes are related to deformations of the Courant bracket which generalize th…
Study finds modular classes help in proving Berezin volumes for supersymmetric theories.
problem Existence of Berezin volumes in supergeometric representation theory.
method Cohomological coherence criterion for modular classes of Q-manifolds.
result Established a method to prove the existence of invariant Berezin volumes.
Vanishing result for supersymmetric model in higher dimensions.
problem Critical points of supersymmetric model on manifolds.
method Proof using Riemannian manifolds, Sobolev inequality, and energy conditions.
result Vanishing of critical points for certain conditions.
The thesis explores dualities and gaugings in supergravity theories.
problem Exploring dualities and gaugings in supergravity theories.
method Analyzing the space of local deformations and the BV-BRST deformation of scalar-vector coupled Lagrangians.
result Only Yang-Mills type deformations are possible for a large class of theories.
Revisits superfields and geometry, offering new formulations and interpretations.
problem Exploring the connection between superfields and geometry.
method Combining different superfield formulations, using a doubled target space, and interpreting equations of motion geometrically.
result Shows that the doubled geometry is Donaldson's deformation of the original Kähler manifold.
A new formula connects supersymmetric path integrals to Chern-Simons theory.
problem Constructing a rigorous path integral for supersymmetric theories on spin manifolds.
method Using Chen differential forms and non-commutative geometry, a Chern-Simons transgression formula is derived.
result The supersymmetric path integral induces a differential topological invariant.
Study connects supermanifold Laplacian to harmonic superfunctions via sigma model.
problem Understanding harmonic superfunctions on supermanifolds.
method Calculus of variations applied to a supersymmetric sigma model.
result Relates Laplacian to harmonic superfunctions on supermanifolds.
Analyzes tt*-structures from -type Stokes data.
problem Classifying tt*-structures over .
method Isomonodromic deformations with upper unitriangular real Stokes matrices.
result Establishes a direct analytic realization of the classification.