Triangle Seminars

Abstract:
In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will review this connection for scattering amplitudes. After a broad introduction and review of the main ingredients involved, I will focus on maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory – the momentum amplituhedron. Finally, I will present some of the main goals and research directions for the future.

Abstract:
Gravitational instantons are four-dimensional, complete, regular and smooth Riemannian manifolds satisfying the Euclidean Einstein equations, which arise naturally in some approaches to quantum gravity. There is a renewed interest in these geometries, thanks to the recent discovery of counterexamples to some famous conjectures, such as Euclidean black hole uniqueness and related problems in Riemannian geometry. After a review of some recent developments focused on the non-hyperkähler case, I will talk about deformations and integrability of the moduli space of ALF instantons.

Abstract:
The average physicist on the street would say that to have a real
energy spectrum and unitary time evolution a quantum Hamiltonian must be Dirac
Hermitian; that is, invariant under complex conjugation + matrix transposition.
However, the non-Dirac-Hermitian Hamiltonian \(H=p^2+ix^3\) has a positive
discrete spectrum and generates unitary time evolution, so \(H\) defines a
consistent physical quantum theory. Thus, Hermiticity symmetry is too
restrictive. While \(H\) is not Dirac Hermitian, it is PT symmetric
(spacetime-reflection symmetric); that is, invariant under parity P + time
reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a
complex generalization of ordinary quantum mechanics. If quantum mechanics
is extended to the complex domain, new theories having remarkable properties
emerge. For example, the Hamiltonian \(H=p^2-x^4\), which has an upside-down
potential, defines two distinct phases, an unstable P-symmetric phase having
complex eigenvalues and a stable PT-symmetric phase whose energy levels are
positive and discrete. The properties of PT-symmetric classical and quantum
systems are under intense study by theorists and experimentalists; many
theoretical predictions have been verified in laboratory experiments.

Abstract:
Sen’s superstring field theory successfully formulates perturbative superstring theory but has a number of strange features.
The action is not fully background independent, and it does not have standard diffeomorphism symmetry - instead there is an exotic gauge symmetry that acts on some fields but not others. These issues greatly restrict the spacetimes that this action can be applied to. A new action is found that reduces to Sen’s in a certain limit, but which has diffeomorphism symmetry together with further exotic symmetries and is background independent. As a result, it can be applied to any spacetime.

Abstract:
I will review some results on semi-classical quantization of M2 branes in AdS4 x  S7/Zk in their relation to dual   ABJM theory  and then  discuss  recent work on computing 2-loop corrections to world-volume S-matrix in superstring  and supermembrane theory.

Abstract:
While strong uniqueness theorems hold for stationary, asymptotically flat black holes in four dimensions, the results break down in higher dimensions and when the asymptotically flat condition is relaxed. Nonetheless, there has been significant progress in classifying the near-horizon geometries of extremal black holes. Motivated by this, we start with near-horizon geometries, which are better understood, and deform them to obtain extremal black hole solutions. We investigate whether a given near-horizon geometry uniquely corresponds to a black hole solution or if there are multiple black holes with the same near-horizon geometry. Our approach employs the homotopy algebraic framework, a powerful and increasingly influential framework in both classical and quantum field theory. Using homological perturbation theory, we recursively solve the deformation problem order by order. To illustrate the method, we present a concrete example of the deformation of the extremal Kerr horizon.

Abstract:
I will review the tensor/matrix model for 2d CFT data subject to crossing constraints, whose topological expansion is proposed to match that of pure 3d gravity. I will discuss various sources of divergences and what remains to prove the correspondence. Then I will turn to a BCFT extension of the model, particularly as associated to a purely open version of the bootstrap. I will explain how the resulting topological expansion is related to gluing tetrahedra, and show how the matrix model captures certain off-shell 3d gravity amplitudes.

Also posted on https://lims.ac.uk/ for more seminar info.