String Theory & Holography

School of Particles and Accelerators Wednesday Weekly Seminar / Hybrid format

Date: Wednesday, Jan 10, 2024 / چهارشنبه، 20 دی 1402 Time: 11:00 AM - 12:00 PM (Tehran time)

Speaker: Mr. Behrad Taghavi

Affiliation: School of Particles and Accelerators, IPM

Title: Classical Liouville Action and Uniformization of Orbifold Riemann Surfaces: A Geometric Approach to Classical Correlation Functions of Branch Point Vertex Operators

Title in Persian:
کنش کلاسیکی لیوویل و یکنواختسازی اُربیسطوح ریمانی: رهیافت هندسی به مطالعه توابع همبستگی کلاسیکی عملگرهای ورتکس متناظر با نقاط شاخهای

Abstract: In this talk, based on arXiv:2310.17536, we will study the classical Liouville field theory on Riemann surfaces of genus g>1 in the presence of vertex operators associated with branch points of orders mi>1. In particular, classical correlation functions of branch point vertex operators on a closed Riemann surface is related to the on-shell value of Liouville action functional on the same Riemann surface but with the insertion of conical points (of angles 2pi/mi) at the location of these operators. With this motivation, and using the results of arXiv:1508.02102 and arXiv:1701.00771, we will study the appropriate classical Liouville action on a Riemann orbisurface using the Schottky global coordinates. Additionally, classical limit of conformal Ward identities motivates us to study the first and second variations of this action on the Schottky deformation space of Riemann orbisurfaces. In this way, we are able to show that the appropriately defined classical Liouville action is a Kähler potential for a special combination of Weil-Petersson and Takhtajan-Zograf metrics which appear in the local index theorem for Riemann orbisurfaces (see arXiv:1701.00771). The obtained results can then be interpreted in terms of the complex geometry of Hodge line bundle equipped with Quillen’s metric over the moduli space of Riemann orbisurfaces. Indico Link: https://indico.hep.ipm.ir/e/b.taghavi

Meeting Place: Seminar Room, School of Particles and Accelerators, IPM

Link to Join Virtually: https://meet.google.com/fnv-dfkk-ghb

School of Particles and Accelerators Theory Weekly Seminar / Virtual Format

Date: Thursday, Jan 11, 2024 / پنجشنبه، 21 دی 1402 Time: 17:30 PM-18:30 PM (Tehran time)

Speaker: Mr. Keivan Namjou

Affiliation: Department of Physics, McGill University

Title: Liouville theory and the Weil–Petersson geometry of moduli space

Title in Persian:
نظریه لیوویل و هندسه ویل_پیترسون فضای ماژولی

Abstract: Conformal field theory is a powerful tool in the study of geometry, with applications ranging from mirror symmetry to spectral theory and quantum chaos. Liouville theory is a specific conformal field theory that provides a natural means to study the Weil–Petersson geometry of the moduli space of Riemann surfaces. In the semiclassical limit, the Liouville path integral computes the Kähler potential, giving access to the metric and associated geometric quantities. In this talk, I will review Liouville theory, the geometry of hyperbolic surfaces and their moduli space, and explain how the study of Liouville theory in the semiclassical limit allows us to describe these geometries.

Link to Join Virtually: https://meet.google.com/fnv-dfkk-ghb

🔸 Next Journal Club Session 🔸

🔹Title: Character preservation property of matrix model

🧑🏻‍🏫 Presenter: Pedram Karimi (Warsaw University)

🕰 Time: 14:‌00 IRST - Monday 18 & 25 December 20‌23
(27 Azar & 04 Day 1402)

📍Location: Ferdowsi University, Faculty of Science, Physics Department, Administration Room

📋 Abstract: Our intention of solving a quantum field theory generally aims to find multi-point functions. In rare cases, we can solve the theory exactly. In all these cases, theories with exact solutions have sets of additional symmetries. The theory of random matrices, as a zero-dimensional field theory, can be solved precisely because of such symmetries. The theory of random matrices is not only solvable, but the solution can be rewritten in a compact form based on special functions, and characters. Such relations, which are known as superintegrability, have their roots in representation theory.
In this lecture, after reviewing the theory of random matrices and symmetric polynomials, a summary of the proof of the character preservation property for Gaussian transformed theorems is presented. Finally, we look at why such relationships exist.
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@sth_fum

🔸 Next Journal Club Session 🔸

🔹Title: Classical Liouville Action and Uniformization of Orbifold Riemann Surfaces: A Geometric Approach to Classical Correlation Functions of Branch Point Vertex Operators

🧑🏻‍🏫 Presenter: Behrad Taghavi (IPM)

🕰 Time: 14:‌00 IRST - Monday 04 December 20‌23 (13 Azar 1402)

📍Location: Ferdowsi University, Faculty of Science, Physics Department, Administration Room

📋 Abstract: In this talk, based on 2310.17536, we study the classical Liouville field theory on Riemann surfaces of genus g>1 in the presence of vertex operators associated with branch points of orders mi>1. In particular, classical correlation functions of branch point vertex operators on a closed Riemann surface are related to the on-shell value of Liouville action functional on the same Riemann surface but with the insertion of conical points (of angles 2pi/mi) at the location of these operators. With this motivation, and using the results of 1508.02102 and 1701.00771, we will study the appropriate classical Liouville action on a Riemann orbisurface using the Schottky global coordinates. We will also study the first and second variations of this action on the Schottky deformation space of Riemann orbisurfaces and show that the classical Liouville action is a Kähler potential for a special combination of Weil-Petersson and Takhtajan-Zograf metrics which appear in the local index theorem for Riemann orbisurfaces (see 1701.00771). The obtained results can then be interpreted in terms of the complex geometry of the Hodge line bundle equipped with Quillen’s metric over the moduli space of Riemann orbisurfaces.
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@sth_fum

لینک شبکه های اجتماعی و راه های ارتباطی گروه ریسمان و هولوگرافی دانشگاه فردوسی مشهد:
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E-mails: sth@um.ac.ir , sth.fum@gmail.com
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