Related papers: The Witten Index Beyond the Adiabatic Approximatio…
We study the limiting behaviour of solutions to abelian vortex equations when the volume of the underlying Riemann surface grows to infinity. We prove that the solutions converge smoothly away from finitely many points. The proof relies on…
In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be…
The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which…
The aim of this paper is to present a comprehensive theory of spintronics phenomena based on the concept of effective gauge field, the spin gauge field. An effective gauge field generally arises when we change a basis to describe system and…
The twisted index of 3d $\mathcal{N}=2$ gauge theories on $S^1 \times \Sigma$ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the…
In this paper, we focus on the moduli space of Seiberg-Witten equation on non-compact manifold with periodic end. Suppose that the scalar curvature on the periodic end is identically zero and the topological conditions: the first de-Rham…
We study N=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include…
Motivated from unified models with string origin, we analyse the constraints from duality invariance on effective supergravity models with an intermediate gauge symmetry. Requiring vanishing vacuum energy and invariance of the…
We study the hyperbolicity of singular quotients of bounded symmetric domains. We give effective criteria for such quotients to satisfy Green-Griffiths-Lang's conjectures in both analytic and algebraic settings. As an application, we show…
The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…
An influential conjecture by Witten states that there is an instanton Floer homology of four-manifolds with corners that in certain situations is isomorphic to Khovanov homology of a given knot $K$. The Floer chain complex is generated by…
By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is…
We study N=1 four dimensional gluodynamics in the context of M-theory compactifications on elliptically fibered Calabi-Yau fourfolds. Gaugino condensates, \theta-dependence, Witten index and domain walls are considered for singularities of…
Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries…
In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (anti-)BRST nilpotent symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing…
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is…
An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry,…
It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to topological gravity in dimension $n \geq 3$. Our choice of the gauge condition for conformal invariance is…
We consider the dynamics of a massless scalar field with time-dependent sources in the adiabatic limit. This is an example of an adiabatic problem without spectral gap. The main goal of our paper is to illustrate the difference between the…
In this paper we extend the nonabelian mirror proposal of two of the authors from two-dimensional gauge theories with connected gauge groups to the case of O(k) gauge groups with discrete theta angles. We check our proposed extension by…