Relativistic Hydrodynamics: A Singulant Perspective

Abstract

As an effective theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. A lot of effort has been devoted to explicit calculations of these coefficients. Here we propose a shift in perspective: we deploy bootstrap techniques to rule out theories that are inconsistent with microscopic causality. What remains is a universal convex geometry in the space of transport coefficients, which we call the hydrohedron. The landscape of all consistent theories necessarily lie inside or on the edges of the hydrohedron. We analytically construct cross-sections of the hydrohedron corresponding to bounds on transport coefficients that appear in sound and diffusion modes for theories without stochastic fluctuations.

Constraining the initial stages of ultrarelativistic nuclear collisions

“…In particular, the gradient expansion has been shown to diverge for this class of solutions [98]. It was also found that the large order behaviour of the gradient series can be expressed in terms of new degrees of freedom, the singulant fields, which track transient effects [62]. The relevance of these advances to the study of attractors remains an interesting challenge for the future.…”

“…The assumption of ultralocality which has lead to Eq. ( 25) is a useful simplification, but it is not strictly obeyed in SYM, and can be avoided at the level of hydrodynamic models [62].…”

Dense Nuclear Matter Equation of State from Heavy-Ion Collisions

“…Within a certain class of models (inspired by the gauge/gravity correspondence), the position-space hydrodynamic expansion (in proper time) around the Bjorken flow within the MIS theory was shown to diverge factorially [551]. In contrast, for the same theory Fouriertransformed into the momentum space there is a finite convergence radius limited by the branch point singularity closest to the origin in the complex momentum plane [567][568][569][570][571]. This inspired the formulation of hydrodynamics far from equilibrium via resummation [572].…”

Locating complex singularities of Burgers’ equation using exponential asymptotics and transseries

“…The more advanced use of transseries, transasymptotic summation and the theory of resurgence is less common in applied mathematics [11][12][13][14][15], although becoming more popular in theoretical physics (see e.g. [16][17][18][19][20][21], as well as [22] and references therein). Here, we apply exponential asymptotics and transseries to locate singularities and zeros of a solution to a second-order ordinary differential equation (ODE) that comes from studying Burgers' equation in a small-time limit, using the method of transasymptotics developed in [23][24][25].…”