Holographic Non-local Rotating Observables and their Renormalization

TL;DR

This paper investigates holographic non-local rotating observables, proposing renormalization schemes to handle their energies, and explores their behavior and dissociation in strongly coupled thermal theories with broken rotational symmetry.

Contribution

It introduces and compares holographic renormalization and mass subtraction schemes for rotating bound states in holography, analyzing their effects in thermal theories with broken symmetry.

Findings

Bound states dissociate at a critical angular frequency.

Less symmetric theories allow bound states to dissociate at lower frequencies.

Numerical solutions show spinning bound states of fixed size with varying frequencies.

Abstract

We analyse non-local rotating observables in holography corresponding to spinning bound states. To renormalize their energies and momenta we suggest and discuss different holographic renormalization schemes motivated by the static non-local observables. Namely the holographic renormalization and the rotating color singlet mass subtraction scheme. In the holographic renormalization we identify the infinite boundary terms and subtract them. In the mass subtraction scheme we evaluate the energy of a spinning trailing string corresponding to the color charged singlet which experiences dragging phenomena and we subtract it from the energy of the bound state to obtain the renormalized finite energy. Then we apply our generic framework to certain strongly coupled thermal theories with broken rotational symmetry. We find numerical solutions corresponding to spinning bound states with a fixed size while varying their angular frequency. By applying numerically the renormalization schemes, we find that there is a critical frequency where the bound state ceases to exist or dissociates. We also note that bound states require lower angular frequencies to dissociate when the theory has less symmetry.