Superpotential

About: Superpotential is a research topic. Over the lifetime, 3836 publications have been published within this topic receiving 137867 citations.

Darboux coordinates, Yang-Yang functional, and gauge theory

Abstract: The moduli space of flat SL 2 connections on a punctured Riemann surface Σ with fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates in which the generating function of the variety of SL 2 -opers is identified with the universal part of the effective twisted superpotential of the corresponding four-dimensional N=2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows defining the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group and relating it to the instanton counting of the four-dimensional gauge theories in the rank-one case.

Phases of N=1 Supersymmetric Gauge Theories with Flavors

Abstract: We explore the phases of N = 1 supersymmetric U(N) gauge theories with fundamental matter that arise as deformations of N = 2 SQCD by the addition of a superpotential for the adjoint chiral multiplet. As the parameters in the superpotential are varied, the vacua of this theory sweep out various branches, which in some cases have multiple semiclassical limits. In such limits, we recover the vacua of various product gauge group theories, with flavors charged under some group factors. We describe in detail the structure of the vacua in both classical and quantum regimes, and develop general techniques such as an addition and a multiplication map which relate vacua of different gauge theories. We also consider possible indices characterizing different branches and potential relationships with matrix models.

4D/3D reduction of dualities: mirrors on the circle

Abstract: We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.

Localisation of field energy

Abstract: The authors define conservation laws in general relativity with respect to a flat reference spacetime, via Noether's theorem and the standard Lagrangian function, quadratic in first-order derivatives. The covariant superpotential obtained in that way fulfils all standard global requirements at spatial and at null infinity and has no anomalous factor of two for the ratio of the mass to angular momentum. Next they attempt to localise the conservation laws and obtain linear and angular momentum densities. They put forward local mapping equations in which a key role is played by a family of artificial, short living, closed shells of matter whose interior is flat. The equations are derived on the basis that the linear momentum densities at each point of the flat interior must be equal to zero. They gain some insight in the mapping equations by considering static spacetimes and spaces with spherically symmetric static shells.