Title: Fun with Mahler Measures

Abstract:

Mahler measures and Ronkin functions have been extensively studied in number theory and also in algebraic geometry. They have later been applied to mathematical and theoretical physics. Since this is an ongoing work, I will mainly review the roles Mahler measures and Ronkin functions play in crystal melting and counting D-brane bound states. If time permits, I will briefly discuss their properties under RG trajectory and dualities in quiver gauge theories as well as their physical implications.

Title: 5d BPS quivers and KK towers

Abstract:

This talk will present recent progress in computing (refined) Witten index of BPS quiver for 5d gauge theories, compactified on a circle. With stringy BPS objects in 5d theory being wrapped on the circle, the wall-crossing problem of 4d KK theory can be addressed by N=4 quiver quantum mechanics. However, the fine-tuned superpotential of the latter makes many of the known machinery fail to capture its Witten indices. I will show how the subtlety can be bypassed for a restricted class of BPS quivers. Specifically, I will construct the entire KK tower of Cartan components in vector multiplets, based on L2 cohomology counting and D0 brane picture. Time permitting, the analysis will be extended to purely electric BPS particles in the weak coupling chamber.

Title: Spins in Lorentzian and Euclidean CFT

Abstract:

In this talk, we will discuss properties of the spin in different signatures of quantum field theory, mostly focus on the conformal field theory. The Euclidean and Lorentizian CFT are connected via the Wick rotation but the behaviour of the spin during the rotation is still not clear. Spin should be an integer in Euclidean signature while it could be real or even complex in Lorentizian signature. And we will illustrate some unsolved questions in our project.

Title: Machine-Learning Plethystics

Abstract:

This talk will review some recent work applying supervised ML techniques to databases of Hilbert Series attempting to predict properties of the underlying projective variety from Taylor coefficients.

Title: Cubic Action in Double Field Theory

Abstract:

We study target space theory on a torus for the states with $N_L+N_R=2$ through Double Field Theory. The spin-two Fierz-Pauli fields are not allowed when all spatial dimensions are non-compact. The massive states provide both non-vanishing momentum and winding numbers in the target space theory. To derive the cubic action, we provide the unique constraint for $N_L\neq N_R$ compatible with the integration by part. We first make a correspondence of massive and massless fields. The quadratic action is gauge invariant by introducing the mass term. We then proceed to the cubic order. The cubic action is also gauge invariant by introducing the coupling between the one-form field and other fields. The massive states do not follow the consistent truncation. One should expect the self-consistent theory by summing over infinite modes. Hence the naive expectation is wrong up to the cubic order. In the end, we show that the momentum and winding modes cannot both appear for only one compact doubled space.

Title: Protected states in AdS/CFT from integrability

Abstract:

We will discuss the description of protected BPS states in AdS3 backgrounds by utilising the integrability of string theory in the planar limit. We will focus on maximally supersymmetric backgrounds, and our result will be valid across the entire moduli space where integrability holds.

Title: Structure of K-theoretic blowup equations

Abstract:

K-theoretic blowup equations were first proposed by Nakajima-Yoshioka for the Nekrasov partition function of 5d pure SU(N) gauge theories. We study the full set of K-theoretic blowup equations for all 5d gauge theories. Our strategy is starting from 5d Kaluza-Klein (KK) theories compactified from 6d SCFTs and translating all elliptic blowup equations to K-theoretic blowup equations. Then we reduce the blowup equations by decoupling one at a time the hypermultiplets in various representations. We find the 5d dualities and flavor enhancement are highly non-trivially reflected in blowup equations.

Title: On the octagon dimer model

Abstract:

Dimer models (aka brane tilings) are bipartite graphs on a torus satisfying some minimality conditions. They encode the structure of 4d N=1 quiver gauge theories living on the worldvolume of D3 branes probing toric affine Calabi-Yau singularities. Wondering whether such setups can incorporate field theories admitting a stable vacuum which breaks supersymmetry dynamically led to stringent combinatorial constraints on the bipartite graphs. We found an instance of a dimer model satisfying these constraints, introduced in hep-th/2005.09671. I will review the background and the construction of this peculiar dimer model using the technology of Thurston's triple crossing diagrams.

Title: Magnetic quivers of 4d and 5d gauge theories

Abstract:

The recently introduced notion of magnetic quiver is a powerful tool in understanding the vacuum structure of supersymmetric gauge theories. Specifically, it encodes the Higgs branch of gauge theories in various dimensions. For 5d N=1 gauge theories, we obtain the magnetic quivers using brane webs consisting of (p,q) 5-branes and 7-branes. Folding the identical legs of these quivers gives magnetic quivers of 4d N=2 theories, including all rank one SCFTs. Once the magnetic quivers are known, a simple algorithm of quiver subtraction reveals the geometric structure of the Higgs branch in the form of a Hasse diagram.