arXiv subjects

Connor Behan

Publications and source records attributed to Connor Behan.

24 records · Page 2Linked to original sources

arXiv2017

A scaling theory for the long-range to short-range crossover and an infrared duality

We study the second-order phase transition in the $d$-dimensional Ising model with long-range interactions decreasing as a power of the distance $1/r^{d+s}$. For $s$ below some known value $s_*$, the transition is described by a conformal field theory without a local stress tensor operator, with critical exponents varying continuously as functions of $s$. At $s=s_*$, the phase transition crosses over to the short-range universality class. While the location $s_*$ of this crossover has been known for 40 years, its physics has not been fully understood, the main difficulty being that the standard description of the long-range critical point is strongly coupled at the crossover. In this paper we propose another field-theoretic description which, on the contrary, is weakly coupled near the crossover. We use this description to clarify the nature of the crossover and make predictions about the critical exponents. That the same long-range critical point can be reached from two different UV descriptions provides a new example of infrared duality.

hep-th↗

arXiv2017

Long-range critical exponents near the short-range crossover

The $d$-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power $1/r^{d+s}$, admits a second order phase transition with continuously varying critical exponents. At $s = s_*$, the phase transition crosses over to the usual short-range universality class. The standard field-theoretic description of this family of models is strongly coupled at the crossover. We find a new description, which is instead weakly coupled near the crossover, and use it to compute critical exponents. The existence of two complementary UV descriptions of the same long-range fixed point provides a novel example of infrared duality.

cond-mat.stat-mech↗

arXiv2014

Simplifying plasma balls and black holes with nonlinear diffusion

In the Master's thesis of the author, we investigate certain aspects of gravitational physics that emerge from stochastic toy models of holographic gauge theories. We begin by reviewing field theory thermodynamics, black hole thermodynamics and how the AdS / CFT correspondence provides a link between the two. We then study a nonlinear evolution equation for the energy density that was derived last year from a random walk governed by the density of states. When one dimension is non-compact, a variety of field theories produce long lived plasma balls that are dual to black holes. This is due to a trapping phenomenon associated with the Hagedorn density of states. With the help of numerical and mathematical results, we show that problems arise when two or more dimensions are non-compact. A natural extension of our model involves a system of partial differential equations for both energy and momentum. Our second model is shown to have some desired, but also some undesired properties, such as a potential disagreement with hydrodynamics.

hep-th↗

arXiv2014

Conformal blocks for highly disparate scaling dimensions

We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via recurrence relations. Connections to the conformal bootstrap program and the AdS / CFT correspondence are also discussed.

hep-th↗

arXiv2013

On the density of states in a free CFT and finite volume corrections

Results from spectral geometry such as Weyl's formula can be used to relate the thermodynamic properties of a free massless field to the spatial manifold on which it is defined. We begin by calculating the free energy in two cases: manifolds posessing a boundary and spheres. The subextensive contributions allow us to test the Cardy-Verlinde formula and offer a new perspective on why it only holds in a free theory if one allows for a change in the overall coefficient. After this we derive an expression for the density of states that takes the form of a Taylor series. This series leads to an improvement over known results when the area of the manifold's boundary is nonzero but much less than the appropriate power of its volume.

hep-th↗

arXiv2013

Energy trapping from Hagedorn densities of states

In this note, we construct simple stochastic toy models for holographic gauge theories in which distributions of energy on a collection of sites evolve by a master equation with some specified transition rates. We build in only energy conservation, locality, and the standard thermodynamic requirement that all states with a given energy are equally likely in equilibrium. In these models, we investigate the qualitative behavior of the dynamics of the energy distributions for different choices of the density of states for the individual sites. For typical field theory densities of states (\log(ρ(E)) ~ E^{α<1}), the model gives diffusive behavior in which initially localized distributions of energy spread out relatively quickly. For large N gauge theories with gravitational duals, the density of states for a finite volume of field theory degrees of freedom typically includes a Hagedorn regime (\log(ρ(E)) ~ E). We find that this gives rise to a trapping of energy in subsets of degrees of freedom for parametrically long time scales before the energy leaks away. We speculate that this Hagedorn trapping may be part of a holographic explanation for long-lived gravitational bound states (black holes) in gravitational theories.

hep-th↗