Timetable
| Time | 09:00-10:00 | break | 10:30-11:30 | Lunch | 14:00-15:00 | break | 15:30-16:30 | break | 17:00-18:00 | 18:00- |
|---|---|---|---|---|---|---|---|---|---|---|
| 26 (Wed) | On-site check-in (also in Thursday morning) | |||||||||
| 27 (Thu) | J-E. Bourgine | M. Huang | H. Kanno | S. Cheng | Discussion | |||||
| 28 (Fri) | K. Ito | M. Dedushenko | S. Komatsu# | J. Wu | R. de Mello Koch | Photo and Dinner | ||||
| 29 (Sat) | P. Koroteev | S. Li | Y. Zhou | K. Hikami | Discussion | |||||
| 30 (Sun) | Departure | |||||||||
(# online talk, part of Theoretical Physics Seminar)
Zoom URL: https://us02web.zoom.us/j/3854420225?pwd=SXY4eWJKOTBFZWJDaE16aXpTamY1QT09
Meeting ID: 385 442 0225, Passcode: yauc
Talks
Jean-Emile Bourgine (SIMIS), Generalized Macdonald polynomials at higher level
Macdonald polynomials can be introduced as eigenstates of the Macdonald Hamiltonian. This operator coincides with a certain element of the quantum toroidal \(gl(1)\) algebra evaluated in the Fock representation of levels (1,0). Representations of higher levels (r,0) produce generalizations of this Hamiltonian, and their eigenstates define generalized Macdonald polynomials. In a joint work with L. Cassia and A. Stoyan, we extend some of the well-known formulas obtained for ordinary Macdonald polynomials to their higher level counterpart. In particular, we propose a generalization of the formula relating Macdonald polynomials to Whittaker vectors obtained by Garsia, Haiman and Tesler. The talk will start with a brief introduction to the notions of Whittaker vectors and reproducing kernels using a toy model. Then, I will introduce Macdonald polynomials and their generalization, and present our main results. I will conclude with a discussion on possible applications to the (q,t)-deformed integrable hierarchies recently introduced with A. Garbali.
Min-xin Huang (USTC), PP-wave Holography and Entropy Bounds
Penrose limit provides a promising avenue to the stringy regime of the AdS/CFT holography, giving rise to the pp-wave background. We propose a probability interpretation of the Berenstein-Maldacena-Nastase (BMN) two-point functions in free N=4 super-Yang-Mills theory in terms of the dual tensionless strings in the infinite curvature limit. If our proposal is correct, it would not only provide the first examples of systematic calculations of the norms of higher genus critical superstring amplitudes, but may also in principle gives exact complete results for any string coupling, due to the convergence of genus expansion. We further provide a definition of the entropy of these BMN strings in the presence of an observer, and derive an entropy bound. Finally, we compare with thermal entropy in Calabi-Yau quantum systems and discuss a possible cosmological application.
Hiroaki Kanno (Nagoya), Super Macdonald polynomials and instanton counting on the blow-up
The super Macdonald polynomials generalize the Macdonald polynomials to the super space with the Grassmann coordinates \(\theta_i\).
They form a basis of a level zero representation of the quantum toroidal algebra of type \(\mathfrak{gl}_{1|1}\).
The Pieri rule of the super Macdonald polynomials is obtained from the action of the raising operators of the algebra.
We show the relation of the Pieri coefficients to the Nekrasov factor for the instanton counting on the blow-up of \(\mathbb{C}^2\).
The talk is based on a collaboration with R.Ohkawa and J.Shiraishi.
Shi Cheng (SIMIS), Surgery and branched cover for 3d theories
Since the discovery of 3d/3d correspondence, three-manifolds are noticed to be a powerful tool to construct 3d N=2 gauge theories, in parallel to Calabi-Yau manifolds. However, both are not completely established yet. In this talk, we focus on the three-manifold approach, which itself also has two parallel methods. One is the surgery of three-manifolds, found by Gadde, Gukov, and Putrov in paper “Fivebranes and 4-manifolds”. Another one is the double branched cover, found by Cecotti, Córdova, and Vafa in “Braids, walls, and mirrors”. In this talk, by using mathematical ideas, we try to complete and unify these two methods.
Katsushi Ito (ISCT), Integrals of Motion and ODE/IM correspondence
The ODE/IM correspondence is the relation between the spectral analysis of ordinary differential equations and the functional relation approach to two-dimensional quantum integrable models. In this talk, I will consider the relation between the linear-differential system associated with an affine Toda field theory based on an affine Lie algebra \(\hat{g}\) and two-dimensional conformal field theory with W-algebra symmetry for its Langlands dual \(\hat{g}^{\vee}\). We calculate the WKB periods for the ODE, which are shown to correspond to the classical conserved currents of the Drinfeld-Sokolov integrable hierarchies. They are shown to agree with the quantum integrable motions of the conformal field theories with W-algebra symmetry. This correspondence provides an exact parameter relation bewteen ODE and IM and a better way of computing of higher integrals of motion in CFT.
Mykola Dedushenko (SIMIS), Quantization by LLL projection, fuzzy hemisphere, and stuff
I will review the recently introduced fuzzy sphere regularization approach to the 3D Ising CFT, including some background material on the fuzzy sphere, and then I'll discuss how one can use the fuzzy hemisphere to study conformal boundary conditions in this model.
Shota Komatsu (CERN), Chiral Composite Linear Dilaton
I will explain the Chiral Composite Linear Dilaton (CLD), a novel worldsheet theory recently introduced. It is a beta-gamma system deformed by a linear-dilaton like action made out of a composite of gamma's. I will explain how observables can be computed by a path integral despite high nonlinearity and highlight applications to string duals of chiral 2d Yang-Mills and symmetric product orbifolds and a worldsheet description of a class of generalized Veneziano amplitudes.
Junbao Wu (Tianjin), Holographic Wilson Loop One-point Functions in ABJM Theory
We compute the correlation function between a circular half-BPS Wilson loop (or straight Wilson line) and a local operator in ABJM theory utilizing its M-theory description. The local operator can be a 1/3-BPS single-trace chiral primary operator or the stress-energy tensor. Using the AdS/CFT correspondence, these correlators are dual to fluctuations of a probe M2-brane in \( AdS_4 \times S^7/Z_k \). We derive analytic results for both cases and compare them with existing results based on supersymmetric localization in the literature. In the large-N limit with k finite, our holograkphic results exhibit perfect agreement with localization. This talk is based on work done with Xiao-Yi Zhang and Yunfeng Jiang.
Robert de Mello Koch (Huzhou), The space of gauge invariant operators at finite N
We argue that the space of invariants of multi-matrix model quantum mechanics, at finite \(N\), is generated by a set of invariants, naturally divided into two distinct classes: primary and secondary. The primary invariants act freely, while secondary invariants satisfy quadratic relations. We argue that the primary invariants correspond to perturbative degrees of freedom, whereas the secondary invariants emerge as non-trivial background structures. The number of primary invariants for a model with d matrices is given by \(1+(d-1)N^2\). The number of secondary invariants grows as \(e^{cN^2}\) at large \(N\), with \(c\) a constant. Finally, we identify a class of light single-trace operators that behave like free creation operators at low energy but saturate beyond a critical excitation level, ceasing to generate new states. This leads to a dramatic truncation of the high-energy spectrum of the emergent theory. The resulting number of independent degrees of freedom is far smaller than naïve semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories.
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Peter Koroteev (BIMSA), On the Quantum K-theory of Quiver Varieties at Roots of Unity
Let \(\Psi(\textbf{z},\textbf{a},q)\) a the fundamental solution matrix of the quantum difference equation of a Nakajima variety \(X\). In this work, we prove that the operator $$ \Psi(\textbf{z},\textbf{a},q) \Psi\left(\textbf{z}^p,\textbf{a}^p,q^{p^2}\right)^{-1} $$ has no poles at the primitive complex \(p\)-th roots of unity \(q=\zeta_p\). As a byproduct, we show that the iterated product of the operators \({\bf M}_{\mathcal{L}}(\textbf{z},\textbf{a},q )\) from the \(q\)-difference equation on \(X\):
$$ {\bf M}_{\mathcal{L}} (\textbf{z} q^{(p-1)\mathcal{L}},\textbf{a},q) \cdots {\bf M}_{\mathcal{L}} (\textbf{z} q^{\mathcal{L}},\textbf{a},q) {\bf M}_{\mathcal{L}} (\textbf{z} ,\textbf{a},q) $$ evaluated at \(q=\zeta_p\) has the same eigenvalues as \({\bf M}_{\mathcal{L}} (\textbf{z}^p,\textbf{a}^p,q^p)\).
Upon a reduction of the quantum difference equation of \(X\) to the quantum differential equation over the field of finite characteristic, the above iterated product transforms into a Grothendieck-Katz \(p\)-curvature of the corresponding quantum connection whreas \({\bf M}_{\mathcal{L}} (\textbf{z}^p,\textbf{a}^p,q^p)\) becomes a certain Frobenius twist of that connection. In this way, we give an explicit description of the spectrum of the \(p\)-curvature of quantum connection for Nakajima varieties.
Si Li (Tsinghua), Holomorphic QFT and Chiral Deformations
We discuss recent developments on ultra-violet finiteness of holomorphic QFT. We discuss two applications. One is about elliptic trace formula for chiral deformations of 2d CFT, and another one on holomorphic Chern-Simons theory in the large N limit.
Yehao Zhou (SIMIS), Stable envelopes for critical loci
In a joint work to appear with Yalong Cao, Andrei Okounkov, and Zijun Zhou, we introduce stable envelopes in critical cohomology and K-theory for symmetric quiver varieties with potentials and related geometries. For tripled quivers with canonical cubic potentials, critical stable envelopes reproduce those on Nakajima quiver varieties, constructed by Maulik and Okounkov. Using the critical stable envelopes, we can construct solutions to Yang-Baxter equations with R-matrixes acting on the critical cohomologies of symmetric quiver varieties with potentials. Then, the FRT formalism gives natural (shifted) (super) Yangian action on these critical cohomologies.
Kazuhiro Hikami (Kyushu), Double affine Hecke algebra and skein algebra
Recent studies reveal a topological property of the double affine Hecke algebra, which is originally developed for symmetric polynomials.I would like to discuss about a relationship between the double affine Hecke algebra and quantum invariants.
Organizers
Ryo Suzuki and Tadashi Okazaki (Southeast University)
Contact address: Contact address: ryosuzuki_at_seu.edu.cn and tadashi.okazaki.hep_at_gmail.com