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Spectral Sum Rules for Conformal Field Theories in Arbitrary Dimension by Justin David

190 views · Published 11 January 2017 · 24:12 · Indexed 25 September 2026

Channel: International Centre for Theoretical Sciences · 2017 · Science & Technology

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11 January 2017 to 13 January 2017

VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru

String theory has come a long way, from its origin in 1970's as a possible model of strong interactions, to the present day where it sheds light not only on the original problem of strong interactions, but also on quantum gravity, black hole physics, hydrodynamics, condensed matter systems and particle physics, besides providing tools to explore new structures in quantum field theory and mathematics.

String theorists from India have played a major role in the development of the subject. The meeting will celebrate the ongoing journey of String theory in the form of exposition and discussion of developments at its frontier. There will be talks by the invited speakers from all around the world covering various frontier areas of string theory.

The talks will broadly cover the following areas:

Black hole physics
Formal developments in String theory
Applications of gauge gravity duality to non-equilibium physics
Supersymmetric quantum field theories
Cosmology
Hydrodynamics
Quantum entanglement
Bose-Fermi dualities and application to condensed matter
Conformal field theory

There will be a special session to felicitate Spenta R. Wadia for his contribution to science and institution-building in India.

CONTACT US
[email protected]

PROGRAM LINK
https://www.icts.res.in/discussion-meeting/STPP2017

Table of Contents (powered by https://videoken.com)
0:00:00 String Theory: Past and Present
0:00:08 Spectral sum rules for conformal field theories in arbitrary dimension 
0:00:25 I was a student of Spenta (1994-1999) during the time of the 2nd string revolution 
0:00:47 The seminars at TIFR were all a buzz with:
0:01:32 All these developments led to a huge amount of literature which appeared on the xxx.lanl listing of abstracts everyday 
0:01:55 It was in this situation working with Spent helped me overcome the crisis of studying superfluous literature.
0:02:30 This advice sounds like any reasonable advisor would give to his student.
0:03:58 The microscopic model (material) is the D1-D5 system. (The word model/models occurs 26 times in this paper)
0:04:25 The detailed study of the properties of the D1/D5 system in light of the AdS/CFT correspondence essentially formed my thesis.
0:04:46 Working with Spenta, through exciting times taught me how crucial it is choose a good model to address the physical question at hand 
0:05:17 I am going talk about how conformal invariance can be used to constrain spectral densities of CFT's at finite temperature.
0:05:57 Introduction 
0:06:47 Sum rules result from analyticity of the 2 point functions in the complex omega-plane.
0:09:33 The diverging term is identical to the one that is obtained for the retarded two point function if the theory is held at zero temperature.
0:10:18 Apply Cauchy theorem and obtain the sum rule on delta G(omega)
0:11:22 To proceed further we need details of the OPE coefficients of the stress tensor:
0:14:50 The coefficient A obtained from the high frequency limit with out the contact terms coincides with the Hofman-Maldacena coefficient.
0:15:19 We are now in a position to state the sum rule. We look at the Greens function
0:15:58 Arutyunov and Frolov (1999)
0:16:57 Let us examine an alternate way of deriving the sum rule holographic
0:17:25 Going through the analysis one evaluates
0:17:53 Remarks: The shear sum rule was first studied in the context of holography in AdS5
0:17:59 Sum Rule and Hofman-Maldacena Variables 
0:20:39 For large N Chern-Simons vector theories Maldacena, Zhiboedov (2012)
0:21:35 The Fourier transform of the OPE in this channel has the structure
0:22:11 Conclusions 
0:22:49 It will be interesting to investigate the other channels in detail, especially holographically.
0:23:30 During the last 10 years, working for building the ICTS, Spent complained to me, that he does not have time to think about the hard questions in physics that he loves 
0:24:06 I wish him more momentous times with physics for the future

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