String excitation energies in SU(N) gauge theories beyond the free-string approximation

Abstract

Abstract:In the presence of a static quark-antiquark pair, the spectrum of the lowlying states in SU(N ) gauge theories is discrete and likely to be described, at large quark separations r, by an effective string theory. The expansion of the excitation energies in powers of 1/r, which derives from the latter, involves an increasing number of unknown couplings that characterize the string self-interactions. Using open-closed string duality, we show that the possible values of the couplings are constrained by a set of algebraic relations. In particular, the corrections of order 1/r 2 must vanish, while the 1/r 3 terms (which we work out for the few lowest levels) depend on a single adjustable coupling only.

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

“…We demonstrate this by reconstructing the full Nambu-Goto action in D dimensions in static gauge starting from the action of D − 2 free massless bosons; we also apply the same method to single boson Lagrangians with generic potential. Next, we use an idea first proposed by Lüscher and Weisz [22] to reconstruct the cylinder partition function of t-deformed rational CFTs, linking the result to the exact g-function formula proposed for massless TBA flows in [23]. The effect of this deformation appears to be easily computable also for other physical observables; the last example we briefly discuss concerns one-point functions on a cylinder geometry.…”

“…To support this conjecture, we will not work in the framework of the exact g-function formula extracted from [23], which would need to be generalized on a case-by-case basis. Instead, we shall adapt an alternative method originally devised by Lüscher and Weisz [22] for free massless bosons in the effective string theory context. This more general and powerful approach is implemented in section 7.2, leading to a confirmation of the Ising model result, which appears to be valid for a generic CFT.…”

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

“…This expression incorporates all the known universal corrections to the flux tube energy, when one expands E(l) in powers of 1/l 2 σ [30][31][32][33][34]. (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].…”

Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

“…Thus the effective string action predicts the spectrum of such closed flux tubes. On the other hand Lorentz invariance constrains the p-dependence of E n (p, l) and this in turn will constrain the possible form of S eff [30,31]. More generally, the conformal invariance of the effective string action [24] can also be used to constrain its form [32,33].…”

“…This corresponds to noting that if we write the effective string action in 'static gauge' and express it in a series of powers of the derivative of the transverse fluctuation field h(x), then the leading Gaussian kinetic term for h gives this universal O(1/l) contribution to E n (l). Much more recently it was found [30] that the next term in the derivative expansion of S eff [h] is universal, so that the next term in an expansion of E n (l), at O(1/l 3 ), is also universal. This was also shown [32,33], at much the same time, and with a stronger result in D = 3 + 1, using the Polchinski-Strominger conformal gauge approach [24].…”