Titles, Abstracts, and Slides

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January 9 (Sat)

Yuya Tanizaki (YITP) [PDF (1.2MB)]

Title: Adiabatic continuity and symmetry-twisting from the viewpoint of anomaly

Abstract: 

It is an important subject to identify ground-state structures of asymptotically-free quantum field theories, but it is usually a tough work due to the strong-coupling nature at low energies. We can make the system weakly coupled at high temperatures, but its phase can be quite different from that of the ground state: Low-temperature states often enjoy non-trivial phenomena such as spontaneous symmetry breaking, but high temperatures typically break such orders. 

In this talk, I will explain symmetry-twisted boundary conditions play an important role to overcome this issue, and we can identify the suitable one from the viewpoint of anomaly matching condition. I will also talk about how this idea is explicitly realized in two-dimensional field theories, and various semiclassical objects, such as fractional instanton, quantum instanton, etc., are essential ingredients of this story. 

Satoshi Yamaguchi (Osaka Univ) [PDF (3.3MB)]

Title: Atiyah-Patodi-Singer index from the domain-wall Dirac operator

Abstract: 

The Atiyah-Patodi-Singer (APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases.  However the APS boundary condition is non-local and hardly realized on the surface of materials.  In this talk, we consider the domain-wall fermion Dirac operator with a local boundary condition, which is naturally given by the kink structure in the mass term.  We propose the relation between the eta invariant of this domain-wall fermion Dirac operator and the APS index. We also give a mathematically rigorous proof of this relation.  

Alexis Roquefeuil (IPMU) [PDF (30MB)]

Title: K-theoretic Gromov--Witten invariants and q-difference equations

Abstract: 

K-theoretic Gromov--Witten invariants are numbers that were defined by Y.-P. Lee in 2004 as the Euler characteristics of some vector bundles on Kontsevich's moduli space of stable maps. Iritani--Milanov--Tonita showed in 2013 that a system of q-difference equations determines genus zero K-theoretic Gromov--Witten invariants.

In this talk, after introducing these concepts, we will show how to use Sauloy's "confluence" of q-difference equations to differential equations in order to produce a comparison between the usual Gromov--Witten invariants and their K-theoretic analogues. We will then discuss the possible analogues of Dubrovin and Gamma conjectures in the K-theoretical setting. The latter is based on a joint work in progress with Todor Milanov.

January 10 (Sun)

Atsushi Takahashi (Osaka Univ) [PDF (108KB)]

Title: Serre dimension and stability conditions

Abstract:

We study the Serre dimension which can be considered as the scaling dimension (or the similarity dimension) of the perfect derived category of a smooth compact dg algebra. It is expected that the infimum of the Ikeda-Qiu's global dimension function on the space of Brideland's stability conditions also gives another "good" notion of dimension. One of our results is that the infimum is always greater than or equal to the Serre dimension.Motivated by the ADE classification of the 2-dimensional N=2 SCFT with c<1, we also give a characterization of the derived category of Dynkin quivers in terms of the Serre dimension and the global dimension function. This is a joint work in progress with Kohei Kikuta and Genki Ouchi.

Kazuya Kawasetsu (Kumamoto Univ)

Title: Free vertex algebras and differential algebras

Abstract:

Vertex algebras are algebraic objects which include chiral symmetry algebras of 2d conformal field theory as examples. Commutative vertex algebras are those with trivial operator product expansions. They are naturally considered as differential algebras. In this talk, we explain vertex algebras and as an application, we use vertex algebra structure to solve a classical question by J. Ritt on differential algebras in 1950. The crucial idea is to consider free vertex algebras, which are first mentioned by R. Borcherds and constructed by M. Roitman.

This talk is based on a joint work with T. Arakawa and J. Sebag.

Takahiro Nishinaka (Ritsumeikan Univ) [PDF (13MB)]

Title: Argyres-Douglas theories, S-duality and AGT correspondence

Abstract:

Argyres-Douglas (AD) CFTs are a series of 4d N=2 superconformal field theories with Coulomb branch operators of fractional scaling dimensions. Since they are strongly coupled, it is hard to compute the partition function of AD CFTs and their cousins via the supersymmetric localization. In this talk, I will discuss computing the partition function of gauge theories involving Argyres-Douglas CFTs in their matter sector, using the generalized AGT correspondence as a tool. Our result is particularly consistent with the S-duality when the gauging is exactly marginal.