Titles, Abstracts and Slides

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January 11 (Sat)

Yutaka Matsuo (Tokyo Univ)

Title: Real topological vertex, boundary state, and quantum toroidal algebra

Abstract:

Some time ago, Krefl, Pasquetti, and Walcher (KPW) proposed a vertex which describes the configuration with D- and O-planes. We introduce a chiral version of the boundary state which describes KPW vertex and shows that it satisfies a certain inter- twining relation between the quantum toroidal algebra and its real version.

Masao Jinzenji (Hokkaido University) [PDF (1.4MB)]

Title: Geometrical proof of generalized mirror transformation of projective hypersurfaces

Abstract:

In this talk, I briefly review my research on ”Classical Mirror Symmetry of Projectve Hypersurfaces”, which began from my graduate student days in Prof. Eguchi’s Laboratory. Then I explain my geometrical proof of Generalized Mirror Transformation of Projective Hypersurfaces.

Tomoyuki Arakawa (RIMS)

Title: 4D/2D duality and Moore-Tachikawa varieties

Abstract:

The 4D/2D duality recently discovered in physics constructs a vertex operator algebra (VOA) as an invariant of a 4 dimensional superconformal field theory with N = 2 supersymmetry (4D N = 2 SCFT). By construction, the VOA computes the Schur index of a 4D N = 2 SCFT as its normalized character. Furthermore, it is conjectured that the VOA recovers the Higgs branch, which is a geometric invariant of a 4D N = 2 SCFT, as its associated variety. In this talk I prove this conjecture for the class of 4D N = 2 SCFTs called the theory of class S.

Masato Taki (RIKEN)

Title:  TBA

January 12 (Sun)

Heng-Yu Chen (National Taiwan University) [PDF (1.8MB)]

Title: The gravity dual of Lorentzian OPE block

Abstract:

In this talk, we consider the operator product expansion (OPE) structure of scalar primary operators in a generic Lorentzian CFT and its dual description in a gravitational theory with one extra dimension. The OPE can be decomposed into bi-local operators transforming as the irreducible representations under conformal group, called the OPE blocks. We show the OPE block is given by integrating a higher spin field along a geodesic in the Lorentzian AdS space-time when the two operators are space- like separated, which can be interpreted as half a geodesic Witten diagram. When the two operators are time-like separated however, we find the OPE block has a peculiar representation where the dual gravitational theory is not defined on the AdS space-time but on a hyperboloid with an additional time coordinate and Minkowski space-time on its boundary. This differs from the surface Witten diagram proposal for the time-like OPE block, but in two dimensions we reproduce it consistently using a kinematical duality between a pair of time-like separated points and space-like ones. This talk is based on paper to appear with Lung-Chuan Chen, Tatsuma Nishoka and Nozomu Kobayashi.

Junichi Shiraishi (Tokyo Univ)

Title: Affine screening operators, affine Laumon spaces, and conjectures concerning non- stationary Ruijsenaars functions

Abstract:

Based on the screened vertex operators associated with the affine screening operators, we introduce the formal power series fglN(x, p|s, κ|q, t) which we call the non-stationary Ruijsenaars function.

We identify it with the generating function for the Euler characteristics of the affine Laumon spaces. When the parameters s and κ are suitably chosen, the limit t → q of fglN(x, p|s, κ|q, t) gives us the dominant integrable characters of slN multiplied by 1/(pN ; pN )∞ (i.e. the gl1 character). Several conjectures are presented for fglN(x, p|s, κ|q, t), including the bispectral and the Poincare dualities, and the evaluation formula. The main conjecture asserts that (i) one can normalize fglN(x, p|s, κ|q, t) in such a way that the limit κ → 1 exists, and (ii) the limit  fst.glN(x, p|s, κ|q, t) gives us the eigenfunction of the elliptic Ruijsenaars operator. The non-stationary affine q-difference Toda operator TglN(κ) is introduced, which comes as an outcome of the study of the Poincare duality conjecture in the affine Toda limit t → 0. The main conjecture is examined also in the limiting cases of the affine q-difference Toda (t → 0), and the elliptic Calogero-Sutherland (q,t → 1) equations.

(Ref. J. Shiraishi, Journal of Integrable Systems, Volume 4, Issue 1, 2019, xyz010)

Kazuhiro Sakai (Meiji Gakuin University) [PDF (5.1MB)]

Title: JT gravity, KdV equations and macroscopic loop operators

Abstract:

We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS2 background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. In this talk I will explain the main framework of our work described above and also several new results including the ’t Hooft expansion, the numerical study of the eigenvalue density and the Baker-Akhiezer function. The talk is based on the joint work [arXiv:1911.01659] with Kazumi Okuyama.

Yasuhiko Yamada (Kobe University) [PDF (76KB)]

Title:  Nekrasov functions and q-difference equations

Abstract:

The AGT relation established the equivalence between 4d Nekrasov partition functions and 2d conformal blocks. When some of the parameters take special values related to degenerate representations, the Nekrasov partition functions give an explicit combinatorial formula for the solutions of linear differential equations (e.g. BPZ equation). In this talk, after reviewing these facts briefly, I will study their q-difference analogs.