Triangle Seminars

Abstract:
AdS/CFT provides a consistent non-perturbative definition of quantum
gravity in asymptotically AdS spacetimes. Black holes correspond to
ensembles of states in the boundary field theory. In the presence of
supersymmetry, we rephrase the problem of counting those states in
terms of a supersymmetric partition function: the superconformal
index. By performing a careful analysis of the index of 4d N=4 SU(N)
Super-Yang-Mills theory, with the help of a Bethe Ansatz approach, we
are able to exactly reproduce the Bekenstein-Hawking entropy of BPS
black holes in AdS5 x S5. The large N limit exhibits many competing
contributions, that we are able to identify with complex saddles of
the (putative) gravitational path-integral. Along the way we propose a
necessary condition for complex saddles to contribute, based on the
size of their non-perturbative corrections.

Abstract:
Machine Learning has opened many new doors in science across multiple
disciplines. Starting from recent work by the speaker and collaborators
on in-depth explorations into the vacuum structure of gauged maximal
supergravities using Machine Learning Technology, notably Google's
TensorFlow library, we subsequently take a broader perspective
on what happens when Machine Learning meets Physics. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

Abstract:
We study the N = 4 SU(N) super-Yang-Mills stress tensor multiplet four-point function at large N and finite complexified Yang-Mills coupling tau, which is dual to the Type IIB graviton correlator on AdS_5 × S^5 at large string length and finite string coupling. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of m, b, and tau of the sphere free energy deformed by mass m and squashing parameter b, which can be computed using supersymmetric localization. We show that at each order in 1/N, these quantities can be written in terms of modular invariants, such as the well studied non-Holomorphic Eisenstein series as well as some new generalizations thereof. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space, which is the first check of AdS/CFT at finite string coupling, and have interesting implications for the structure of the analogous expansion in AdS_5 × S^5.


Zoom

Join Zoom Meeting
https://zoom.us/j/93725965823?pwd=Q2lmeEhjQnJmZUsxMkp2THdVZ1cxUT09

Meeting ID: 937 2596 5823
Passcode: 640955

Abstract:
[For zoom details please email s.nagyATqmul.ac.uk There will be a pre-seminar for students at 13:30]
Knot theory plays an important role in physics, mathematics and biology. Characterizing knots is, however, a difficult task. There are different ways to represent a knot (e.g. via braids, Gauss codes, Dowker-Thistlethwaite notation), and many knot invariants exist (e.g. the Alexander polynomial, Jones polynomial, determinant, slice genus). However, it is not known whether these can be used to identify a trivial knot, the so-called unknot.
We use different machine learning techniques to tackle this question. First, we use a very recent neural network architecture developed for natural language processing, called the reformer, to decide whether a given knot is the unknot. We also apply Reinforcement Learning to solve the harder problem of finding a set of Reidemeister/Markov moves that explicitly simplify a given knot as much as possible. If the algorithm finds a sequence of moves that removes all crossings of a knot in a given representation, then this knot is provably the unknot.

Abstract:
The behavior of dynamical correlation functions in one-dimensional quantum systems at zero temperature is now very well understood in terms of linear and non-linear Luttinger models. The "microscopic" justification of these models consists in exactly accounting for the soft-mode excitations around the vacuum state and at most a few high-energy excitations. At finite temperature, or more generically for finite entropy states, this direct approach is not strictly applicable due to the different structure of soft excitations. To address these issues we study the asymptotic behavior of correlation functions in one-dimensional free fermion models. On the one hand, we obtain exact answers in terms of Fredholm determinants. On the other hand, based on "microscopic" numerical resummations, we develop a phenomenological approach that provides results depending only on the state-dependent dressing of the scattering phase. Our main example will be the sine-kernel and correlation functions in XY model.
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