6533b7dbfe1ef96bd1270cd0
RESEARCH PRODUCT
Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics
Vladimir KazakovVladimir KazakovSebastien LeurentSebastien LeurentSebastien Leurentsubject
High Energy Physics - TheoryNuclear and High Energy PhysicsSigma modelField (physics)FOS: Physical sciences2 dimensionsrepresentation-theory01 natural sciencesexcited-state energiesnonlinear integral-equationsQuantum mechanics0103 physical sciencesBound statelcsh:Nuclear and particle physics. Atomic energy. Radioactivityvolume dependenceQuantum field theory010306 general physicsS-matrixMathematical physicsPhysics[PHYS]Physics [physics][ PHYS ] Physics [physics]010308 nuclear & particles physicsWronskiano(n) sigma-modeln phase-transitionState (functional analysis)goldstone bosonsAdS/CFT correspondenceHigh Energy Physics - Theory (hep-th)lcsh:QC770-798tba equationsdescription
Using recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L, we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)xSU(N) principal chiral field model as functions of m L, where m is the mass scale. We propose a determinant solution of the underlying Y-system, or Hirota equation, in terms of determinants (Wronskians) of NxN matrices parameterized by N-1 functions of the spectral parameter, with the known analytical properties at finite L. Although the method works in principle for any state, the explicit equations are written for states in the U(1) sector only. For N>2, we encounter and clarify a few subtleties in these equations related to the presence of bound states, absent in the previously considered N=2 case. In particular, we solve these equations numerically for a few low-lying states for N=3 in a wide range of m L.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |