arXiv research

Study rigid limit of hypermultiplet moduli spaces in string theory.

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

Given a J-holomorphic Morse function on a symplectic manifold, a new construction of the Fukaya-Seidel category is outlined. Applying this construction in an infinite dimensional case, a Fukaya-Seidel-type category is associated to a smooth three-manifold. In this case the construction is based on a five-dimensional ga…

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 find a Sasaki-Einstein metric from a CFT state in AdS5.

We consider Spin(4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form $M^d \times T^{1,1}$, where $M^d$ is a smooth manifold and $T^{1,1}$ is a five-dimensional Sasaki-Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on $M^d$ extending those induced via reduction over th…

In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and five-dimensional manifolds with boundary, with a rather subtle boundary condition …

The paper explores Kaluza-Klein theories without assuming a fibration structure.

5D SCFTs can have confining vacua with strings and unbroken symmetries.

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geode…

Study shows how black hole horizons relate to specific Einstein-Cartan-Weyl structures.

Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperkähler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their moduli spaces can be identified, on the one hand, with Coulomb branches of five-dimens…

New equations simplify gauge-theoretic Khovanov homology solutions.

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

Study of 5D SYM theory on toric surfaces yields refined Vafa-Witten invariants.

We consider the issue of the slice invariance of refined topological string amplitudes, which means that they are independent of the choice of the preferred direction of the refined topological vertex. We work out two examples. The first example is a geometric engineering of five-dimensional U(1) gauge theory with a ma…

We find canonical gauges for higher gauge theories in 2- and 3-gauge theories.

We show a duality which arises from distributions of Cartan type, having growth (2, 3, 5), from the view point of geometric control theory. In fact we consider the space of singular (or abnormal) paths on a given five dimensional space endowed with a Cartan distribution, which form another five dimensional space with a…

We construct a versal family of deformations of CR structures in five dimensions, using a differential complex closely related to the differential form complex introduced by Rumin for contact manifolds.

We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…

Lecture notes on gauge theory for manifold invariants.

New discretization method for gauge theories preserves gauge invariance rigorously.

A left invariant Z-Randers metric on the five-dimensional Heisenberg group is a left invariant Randers metric with deformation vector from the center of the Heisenberg algebra. In this note we prove that for every left invariant Z-Randers metric on the five-dimensional Heisenberg group there exist flags of strictly neg…

We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved $A_{\infty}$-structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…

New classification of 5D nilsolitons using algebraic Ricci soliton equation.

Gauge theory for families helps compare 4-manifold groups.

Paper classifies Schouten-like metrics on 5D nilpotent Lie groups.

We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically buil…

Survey of gauge theory for families of 4-manifolds.

Higher gauge theory via differential nonabelian cohomology

Survey on advanced gauge theory concepts.

In the first part of this paper, we work out a perturbative Lagrangian formulation of semistrict higher gauge theory, that avoids the subtleties of the relationship between Lie 2-groups and algebras by relying exclusively on the structure semistrict Lie 2-algebra v and its automorphism 2-group Aut(v). Gauge transformat…

Develops a new approach to describe gauge theories with background fields using presymplectic structures.

Develops a new sampling method for gauge theories.

Defines mathematical Coulomb branches for 3D gauge theories.

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and…

It is argued that the enlargement of the gauge group found in non-commutative gauge theory is more fundamentally thought of as a consequence of the non-locality of the construction and that it was already encountered in an earlier discussion of a non-local gauge theory.

We study the relation between the space of representation classes of the fundamental group of a Riemann surface and gauge theory on trivalent graphs. We construct a partial gauge fixing in the latter gauge theory. As an application we get a proof of a conjecture of Florentino.

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such as gauge theory, lattice gauge fields, equivariant bundles, etc. In the course o…

Extends Coulomb gauge existence to non-associative gauge theory.

The study classifies all compact 5D polytopes with 9 facets.

A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of t…

New method for non-abelian parallel transport in higher gauge theories.

In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In both cases the scalar manifold of the reduced theory is described as an eight-di…

Study gauge groups over high-dimensional manifolds, showing homotopy decompositions.

Finite presentations for skein algebras linked to gauge field theory.

Study non-Abelian gauge theories using Poisson bracket structures.

We obtain minimal dimension matrix representations for each indecomposable five-dimensional Lie algebra over $\R$ and justify in each case that they are minimal. In each case a matrix Lie group is given whose matrix Lie algebra provides the required representation.