A symmetry principle for emergent spacetime

There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm requires some sort of symmetry principle or order parameter that captures its appearance. In this essay, we propose higher-form symmetries as a symmetry principle underlying emergent spacetime. We explore higher-form symmetries in gauge–gravity duality and explain how their breaking describes features of gravitational theory. Such symmetries imply the existence of nonlocal objects in the gravitational theory — in gauge–gravity duality these are the strings and branes of the bulk theory — giving an alternative way to understand the nonlocality necessary in any ultraviolet completion of gravity.

Steady States, Thermal Physics, and Holography

It is well known that a Rindler observer measures a nontrivial energy flux, resulting in a thermal description in an otherwise Minkowski vacuum. For systems consisting of large number of degrees of freedom, it is natural to isolate a small subset of them and engineer a steady state configuration in which these degrees of freedom act as Rindler observers. In Holography, this idea has been explored in various contexts, specifically in exploring the strongly coupled dynamics of a fundamental matter sector, in the background of adjoint matters. In this article, we briefly review some features of this physics, ranging from the basic description of such configurations in terms of strings and branes, to observable effects of this effective thermal description.

MCMC with strings and branes: The suburban algorithm (Extended Version)

Motivated by the physics of strings and branes, we develop a class of Markov chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a collection of parallel Metropolis–Hastings (MH) samplers, we place them on an auxiliary grid, and couple them together via nearest neighbor interactions. This leads to a class of “suburban samplers” (i.e. spread out Metropolis). Coupling the samplers in this way modifies the mixing rate and speed of convergence for the Markov chain, and can in many cases allow a sampler to more easily overcome free energy barriers in a target distribution. We test these general theoretical considerations by performing several numerical experiments. For suburban samplers with a fluctuating grid topology, performance is strongly correlated with the average number of neighbors. Increasing the average number of neighbors above zero initially leads to an increase in performance, though there is a critical connectivity with effective dimension [Formula: see text], above which “groupthink” takes over, and the performance of the sampler declines.

A brief review of E theory

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

A unified description of particles, strings and branes in Clifford spaces and p-brane/polyparticle duality

It is described how the Extended Relativity Theory in [Formula: see text]-spaces (Clifford spaces) allows a unified formulation of point particles, strings, membranes and [Formula: see text]-branes, moving in ordinary target spacetime backgrounds, within the description of a single polyparticle moving in [Formula: see text]-spaces. The degrees of freedom of the latter are provided by Clifford polyvector-valued coordinates (antisymmetric tensorial coordinates). A correspondence between the [Formula: see text]-brane ([Formula: see text]-loop) “Schrödinger-like” equations of Ansoldi–Aurilia–Spallucci and the polyparticle wave equation in [Formula: see text]-spaces is found via the polyparticle/[Formula: see text]-brane correspondence. This correspondence might provide another unexplored avenue to quantize [Formula: see text]-branes (a notoriously difficult and unsolved problem) from the more straightforward quantization of the polyparticle in [Formula: see text]-spaces, even in the presence of external interactions. We conclude with comments about the compositeness nature of the polyvector-valued coordinate operators in terms of ordinary [Formula: see text]-brane coordinates via the evaluation of [Formula: see text]-ary commutators.