I will describe a method for approximately solving the crossing equations in a general CFT, using Reinforcement Learning as a stochastic optimiser. I will then present an application of this approach in the context of the 6D (2,0) theory.

I will describe a method for approximately solving the crossing equations in a general CFT, using Reinforcement Learning as a stochastic optimiser. I will then present an application of this approach in the context of the 6D (2,0) theory

This is the live session included as part of the LonTI lecture on the Superconformal Index. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. The superconformal index is a very useful tool that allows us to probe the protected spectrum of a superconformal field theory (SCFT). After a brief review of the construction of unitary irreducible representations of the superconformal algebra, I will then motivate and give its definition for generic SCFTs before specialising to 4D N=2. Special limits of the index with additional supersymmetry, as well as applications will also be discussed. No prior knowledge of the topic is required.

This recorded tutorial is available via youtube at https://youtu.be/L-C6Xx0uI3c. The superconformal index is a very useful tool that allows us to probe the protected spectrum of a superconformal field theory (SCFT). After a brief review of the construction of unitary irreducible representations of the superconformal algebra, I will then motivate and give its definition for generic SCFTs before specialising to 4D N=2. Special limits of the index with additional supersymmetry, as well as applications will also be discussed. No prior knowledge of the topic is required.

It is often said that soliton contributions to perturbative processes in QFT are exponentially suppressed by a form-factor. We will provide a derivation of this form-factor by studying the soliton-antisoliton pair-production amplitude. This reduces to the calculation of a matrix element in the quantum mechanics on the soliton moduli space. We will investigate the conditions under which the latter leads to suppression. Extending this framework to instanton-solitons in five-dimensional Yang-Mills theory leaves open the possibility that such contributions will not be suppressed.

We revisit the relationship between the 6D (2, 0) M5 CFT compactified on a circle to 5D maximally supersymmetric YM Gauge Theory. We show that in the broken phase 5D SYM contains a spectrum of soliton states that can be identified with the complete KK modes of an M2 ending on the M5's. This provides evidence that the (2,0) theory on a circle is equivalent to 5D SYM with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

We revisit the relation of the six-dimensional (2, 0) M5-brane Conformal Field Theory compactified on a circle to 5D maximally supersymmetric Yang-Mills Gauge Theory. We show that in the broken phase 5D super-Yang-Mills contains a spectrum of soliton states that can be identified with the complete Kaluza-Klein modes of an M2-brane ending on the M5-branes. This provides evidence that the (2,0) theory on a circle is equivalent to 5D super-Yang-Mills with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional super-Yang-Mills theory along with six-dimensional abelian (2,0) tensor multiplets. Possible applications to D4-branes and M5-branes are discussed.

We will discuss how by integrating out a global U(1)B gauge field, the U(n)xU(n) ABJM models at level k are equivalent to SU(n)xSU(n) N=6 Chern-Simons theories with a Zk identification on the fields and a modified flux quantisation condition, but only when n and k are relatively prime. As a consequence, the ABJM model for two M2-branes in R8 can be identified with the N=8 SU(2)xSU(2) theory at k=1. We will also argue that the original N=8 SO(4)-theory of Bagger and Lambert, without modified flux quantisation, is equivalent to the U(2)xU(2) ABJM model at k=2 and hence describes the IR fixed point of a maximally supersymmetric three-dimensional O(4) gauge theory obtained in M-theory by an R8/Z2 orbifold without torsion.

I will be reviewing the details of a novel form of the Higgs mechanism, present in the context of the Bagger-Lambert and ABJM proposals for the worldvolume description of multiple parallel M2 branes. I will also discuss some of its implications as well as describe related applications. The latter will focus on the determination of four-derivative corrections to the Bagger-Lambert A_4-theory for all values of the Chern-Simons level k