Quantisation of the effective string with TBA

Abstract

In presence of a static pair of sources, the spectrum of low-lying states of whatever confining gauge theory in D space-time dimensions is described, at large source separations, by an effective string theory. In the far infrared the latter flows, in the static gauge, to a two-dimensional massless free-field theory. It is known that the Lorentz invariance of the gauge theory fixes uniquely the first few subleading corrections of this free-field limit. We point out that the first allowed correction -a quartic polynomial in the field derivatives -is exactly the composite field TT , built with the chiral components, T andT , of the energy-momentum tensor. This irrelevant perturbation is quantum integrable and yields, through the thermodynamic Bethe Ansatz (TBA), the energy levels of the string which exactly coincide with the Nambu-Goto spectrum. We obtain this way the results recently found by Dubovsky, Flauger and Gorbenko. This procedure easily generalizes to any two-dimensional CFT. It is known that the leading deviation of the Nambu-Goto spectrum comes from the boundary terms of the string action. We solve the TBA equations on an infinite strip, identify the relevant boundary parameter and verify that it modifies the string spectrum as expected.

SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement

“…(4.3) encodes all the finite-l corrections that are significant, at our value of l, given our errors. As remarked earlier, this is to be expected since we know that all correction terms to σl up to O(1/l 5 ) are universal [30][31][32][33][34][37][38][39][40][41][42][43] flux tubes and these terms are precisely what one obtains when expanding the Nambu-Goto expression in powers of 1/σl 2 . Of course when the flux tube is not stable it is not clear that it should be described by an effective string action, and here our numerical tests in SO (3) and SO (5) are useful.…”

“…(See also [35,36].) It has also been shown to arise as a good approximation at small l from the near-integrability of the world-sheet action [37][38][39][40][41][42][43]. Moreover it has been checked numerically with some precision in SU(N ) for flux tubes carrying both fundamental and higher representation fluxes.…”

T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed 2D quantum field theories

“…This idea was readily adapted in [9] to encompass the open string case, a framework more directly relevant to the study of the quark-anti-quark potential. In the same paper, the setup was generalised to describe the deformation, via the same CDD factor, of an arbitrary 2D conformal field theory (CFT).…”

“…The CDD factor (1.2) was introduced in [20] as a generalization of the proposal of [6] to theories with more than one particle species. It was first pointed out in [9] that this deformation corresponds to perturbing the CFT theory with a series of irrelevant operators whose leading term is TT. As we shall discuss in this paper, the introduction of the phase factor in the nonlinear integral equations describing the spectrum at finite-size leads to a characteristic deformation of the energy levels as t is varied, which flows according to the inviscid Burgers equation of hydrodynamics.…”

T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ and LST

“…In this section we discuss some aspects of the recent work [4,5] (see also [6,7]) on the theory obtained by deforming the Lagrangian of a two dimensional conformal field theory JHEP07(2017)122…”