Remarks 1 and 2 focus on half-BPS line defects in four-dimensional field theories with N=2 supersymmetry. Remark 1 concerns a minor, but intriguing, gap in the classification of line defects in Lagrangian theories of class S. Remark 2 concerns computations of ``VEV's'' of line defects on R3 x S1. Remark 3 discusses some hypothetical new N=2 d=4 superconformal theories.
Brane Brick models are 2d (0,2) gauge theories on the world-volume of D1-branes probing toric Calabi-Yau (CY) 4-fold singularities. Given a toric diagram, we can construct the gauge theory by orbifolding, partial resolution, or other means. For abelian theories, we can verify that the classical moduli space coincides with the CY geometry, most efficiently by using a combinatorial tool called...
I will consider 4d N=1 supersymmetric theories on a compact Euclidean manifold of the form S1×S3. Taking the limit of shrinking S1, I will present a formula for the limit of the localization integrand, derived by simple effective theory considerations. The limit is given in terms of an effective potential for the holonomies around the S1, whose minima determine the asymptotic behavior of the...
Argyres-Douglas (AD) theory is an N=2 superconformal field theory (SCFT) which has no weak-coupling limit. Nevertheless, AD theory is believed to be the simplest interacting N=2 SCFT. In this talk, I will present N=1 gauge theories that flow to the AD theory and its generalizations in the IR. This high-energy description of the AD theory makes it possible to compute supersymmetric partition...
[Colloquium.] I will explain the meaning of the two phrases in the title. Much of the talk will be a review of the renowned Seiberg-Witten formulation of the low-energy physics of certain four dimensional supersymmetric interacting quantum field theories. In the latter part of the talk I will briefly describe some of the significant progress that has been made in solving for the so-called BPS...
We calculate the masses of the D2 and and D4 brane at the conifold of one parameter Calabi-Yau spaces, using the motivic Hodge conjecture. This gives evidence for the latter in a new context.
We study the enumerative relationship between local and log Calabi-Yau geometries for del Pezzo surfaces. Genus zero log BPS numbers for del Pezzo surfaces are defined from the log Calabi-Yau geometry of the surface with a smooth anticanonical divisor. We propose their conjectural relationship to the genus zero local BPS state counts. This talk is based on joint work with Michel van Garrel,...
I will describe two GLSMs with gauge group U(2), that help to understand geometry of a hyper-kähler 4-fold and of an abelian surface (varieties of lines on del Pezzo manifolds). By RG flow one can relate sigma-models on these CYs to "symmetric squares" of smaller theories, despite the fact that for very general cubic fourfold its variety of lines is not birational to a Hilbert scheme of a K3 surface.
In this talk I will discuss 3d gauge theories with monopole operator entering the superpotential. Starting with the theory without monopole potential, if the monopole potential is relevant there is an RG flow to the monopole-deformed theory. Here, focusing on U(Nc) SQCD with Nf flavors and N=2 supersymmetry, I will argue that even when the monopole potential is irrelevant, the...
I will prove the holomorphic anomaly equation for stable quotient invariant of local P2. This equation is in the precise form predicted by B-model physics. If I have more time, I will also explain about the holomorphic anomaly equation for [C3/Z3] and formal quintic invariants. This talk is based on joint work with Rahul Pandharipande.
In the late 80s and early 90s a three-way link was established between N=(2,2) SCFTs, compact Calabi Yau (CY) manifolds, and modular/Jacobi forms. These links can be understood through the corresponding Gauged Linear Sigma Models and calculations of their elliptic genera. I will discuss how there are interesting modifications to these links when the spectrum involves a continuum. The...
Three-dimensional gauge theories with eight supercharges (3d N=4) have a rich moduli space of supersymmetric vacua with different low energy physics. This infrared physics is well understood for theories with large enough number of flavours ("good theories"), but less so if the number of flavours is small ("bad theories"). In this talk I will focus on 3d N=4 super-QCD theories with U(N) gauge...
Many of the gauged dynamics motivated by string theory come with gapless asymptotic directions. In this talk, we focus on d=1 GLSM's of such kind and their Witten indices, having in mind of the associated D-brane bound state problems. Upon illustrating by examples that twisted partition functions can be misleading, we proceed to explore how physical Witten indices can sometimes be embedded...
I will talk about three-dimensional N=2 supersymmetric gauge theories on M_{g,p}, a circle bundle of degree p over a genus g Riemann surface. We compute the supersymmetric partition functions on M_{g,p} and correlation functions of BPS loop operators. We also consider four-dimensional uplift of this construction, which computes the generalized index of N=1 gauge theories defined on elliptic...
Using the modular bootstrap, we study the constraints on the spectrum of c>1 unitary two-dimensional conformal field theories with holomorphic currents. Imposing a gap in the twist, we obtain the numerical upper bound on conformal dimension of the lowest primary states. We find that diverse rational conformal field theories are realized on the numerical boundary, including the level-1...
We discuss the reduction of supersymmetric theories to two dimensions, and new features that arise here, including non-trivial target space metrics and the appearance of direct sums of decoupled theories. We describe how these features affect the reduction of supersymmetric dualities, and point out new subtleties that arise in two dimensional infrared dualities. In the process, we recover...
[Colloquium.] Dualities give us new perspectives on the dynamics of supersymmetric gauge theories and are valuable tools to explore the strongly coupled phases. We know different types of dualities such as holographic, UV and IR dualities and various examples of correspondences relating supersymmetric gauge theories to lower-dimensional theories such as 2d CFTs. Over the last 10 years the...
It is an often noted fact that the vast majority of known Calabi-Yau geometries admit a genus one fibration. I will investigate this in the context of Calabi-Yau described as complete intersections in products of projective spaces, as well as extensions of that construction. The vast majority of these manifolds admit a large number of different fibrations. We will use this structure to...
Abstract: Superconformal field theories placed in nontrivial background fields for the metric and the continuous global symmetries exhibit a rich web of RG flows across dimensions. I will discuss several examples of such flows and emphasize some of their universal features. In addition, I will employ non-perturbative tools such as 't Hooft anomaly matching, a-, F-, and c-extremization, and...
Perturbative series in quantum field theory is typically divergent.
There is a standard way to resum divergent series called Borel resummation. While perturbative series in typical field theory is expected to be non-Borel summable, it is natural to ask when perturbative series is Borel summable and if it is non-Borel summable, what is a correct way to resum the perturbative series. In my talk...
I will discuss supersymmetric AdS_3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d N=(0,4) superconformal field theories with small superconformal algebra. The aim of this work is to set up holography in the context of F-theory, which are traditionally two distinct areas of string theory. The talk will be based on the arXiv...
