QCD β -function on the string worldsheet

Abstract

We consider confining strings in pure gluodynamics and its extensions with adjoint (s)quarks. We argue that there is a direct map between the set of bulk fields and the worldsheet degrees of freedom. This suggests a close link between the worldsheet S-matrix and parton scattering amplitudes. We report an amusing relation between the Polchinski-Strominger amplitude responsible for the breakdown of integrability on the string worldsheet and the Yang-Mills β-function b0 = Dcr − D ph 6 .Here b0 = 11/3 is the one-loop β-function coefficient in the pure Yang-Mills theory, Dcr = 26 is the critical dimension of bosonic strings and D ph = 4 is the dimensionality of the physical space-time we live in. A natural extension of this relation continues to hold in the presence of adjoint (s)quarks, connecting two of the most celebrated anomalies-the scale anomaly in quantum chromodynamics (QCD) and the Weyl anomaly in string theory.Our description of strong interactions is embarrassingly incomplete without understanding of strings (flux tubes) responsible for quark confinement. The stringy nature of the real world QCD manifests itself through the existence of Regge trajectories-families of hadrons following a quadratic relation between the spin J and the mass M ,s is the string tension. Critical string theory was born exactly 50 years ago [1] as an effort to explain this behavior. Theoretical and lattice studies of confining strings are natural to perform in a more pristine environment obtained by eliminating dynamical quarks in the fundamental representation of the gauge group SU (N c ). As a result, strings do not break and one may study dynamics of an isolated infinitely long flux tube. In lattice simulations a long string state is created by the Polyakov loop operator [2]wrapped around one of the spatial directions.In the planar limit [3], N c → ∞, the worldsheet excitations decouple from bulk degrees of freedom and define a microscopic two-dimensional theory. Importantly, the worldsheet theory itself remains interacting even in the strict planar limit. Furthermore, there is mounting evidence that the worldsheet dynamics is not described by a conventional local quantum field theory, but rather exhibits characteristic features of a gravitational theory [4].Much of the recent progress is triggered by identification of the worldsheet S-matrix as a primary fundamental observable [5]. This S-matrix is a natural theoretical target and at the same time has proven itself as an indispensable tool for the analysis of lattice data [6,7].Current lattice results [8][9][10][11][12][13] (see [14,15] for reviews) for both D = 4 and D = 3 gluodynamics can be summa-rized by the Axionic String Ansatz (ASA) [16,17]. According to the ASA the only stable asymptotic degrees of freedom on the confining string are massless Goldstone excitations X i (i = 1, . . . , D − 2) associated with spontaneous breaking of translations in the presence of a long string. In addition, worldsheet scattering at D = 4 exhibits a metastable resonance-the worldsheet ax...

Undressing confining flux tubes with TT¯

“…In order to obtain the two particle amplitude we also need to extract the undressed phase shift from the data to determineR in (27). This can be done from the ABA equation (16).…”

“…This approach allowed to identify a massive pseudoscalar resonance ("the worldsheet axion") on a worldsheet of D = 4 confining strings and led to the Axionic String Anstaz (ASA) [25][26][27] for the structure of the worldsheet theory both at D = 3 and D = 4. To make further use of lattice data one needs to extend this approach to multiparticle states and find a systematic way to incorporate higher order non-integrable corrections to the worldsheet scattering.…”

Yang-Mills glueballs as closed bosonic strings

“…Coming from a theory side, low energy integrability arises as a consequence of the tree level integrability of the Nambu-Goto theory [13]. At high energies integrability can be understood as a byproduct of asymptotic freedom and confinement [14]. Namely, it is natural to identify high energy degrees of freedom on the worldsheet with partons.…”

Confining strings, infinite statistics, and integrability

“…The successes of ASA have a clear physical origin [20,27]. At low energies the worldsheet degrees of freedom are translational Goldstone bosons of the nonlinearly realized Poincaré symmetry [5,[28][29][30][31][32].…”