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A bstract We study the mass-deformed sphere free energy of three-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals. Building on previous observations, we conjecture a proportionality relation between the sphere free energy on the boundary and the prepotential of the four-dimensional $$ \mathcal{N} $$ N = 2 supergravity theory in the bulk. We verify this formula by explicit computation in several examples of supergravity theories with vector multiplets and hypermultiplets.
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The constraining power of Coulomb Branch Geometry: lectures on Seiberg-Witten theory
The constraining mathematical structure of the Coulomb branch of four dimen- sional N = 2 supersymmetric theories is discussed. The presentation follows a somewhat different route from other excellent reviews on the subject and it is geared towards using this tool to classify four dimensional N = 2 superconformal field theories. This is the writeup of the lectures given at the Winter School “YRISW 2020” to appear in a special issue of JPhysA.
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- Award ID(s):
- 1914679
- PAR ID:
- 10339031
- Date Published:
- Journal Name:
- YRISW 2020
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A bstract It is known that some theories of class S are actually factorized into multiple decoupled nontrivial four-dimensional $$ \mathcal{N} $$ N = 2 theories. We propose a way of constructing examples of this phenomenon using the physics of half-BPS surface defects, and check that it works in one simple example: it correctly reproduces a known realization of two copies of $$ \mathcal{N} $$ N = 2 superconformal SU(2) QCD, describing this factorized theory as a class S theory of type A 3 on a five-punctured sphere with a twist line. Separately, we also present explicit checks that the Coulomb branch of a putative factorized class S theory has the expected product structure, in two examples.more » « less
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A bstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition . This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper. This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.more » « less
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null (Ed.)A bstract New renormalisation group flows of three-dimensional Chern-Simons theories with a single gauge group SU( N ) and adjoint matter are found holographically. These RG flows have an infrared fixed point given by a CFT with $$ \mathcal{N} $$ N = 3 supersymmetry and SU(2) flavour symmetry. The ultraviolet fixed point is again described by a CFT with either $$ \mathcal{N} $$ N = 2 and SU(3) symmetry or $$ \mathcal{N} $$ N = 1 and G 2 symmetry. The gauge/gravity duals of these RG flows are constructed as domain-wall solutions of a gauged supergravity model in four dimensions that enjoys an embedding into massive IIA supergravity. A concrete RG flow that brings a mass deformation of the $$ \mathcal{N} $$ N = 2 CFT into the $$ \mathcal{N} $$ N = 3 CFT at low energies is described in detail.more » « less
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