We present a major update on the spectrum of closed flux tubes in $D=3+1$ $SU(N)$ gauge theories. We measure the excitation spectrum of confining strings wound around a spatial dimension of a size $R$. We do so for the $SU(N)$ Yang-Mills theory with $N=3,5,6$ and for two different values of the lattice spacing. We employ the generalized eigenvalue problem in combination with an extended basis of operators; this enables us to project onto all possible irreducible representations characterised by spin $|J_{\rm modulo \ 4}|$, transverse parity $P_{\perp}$, longitudinal parity $P_{\parallel}$ as well as by longitudinal momentum $p_{\parallel}=\frac{2 πq}{R}$, and extract accurate results for approximately $35$ lightest states. Applying the Thermodynamic Bethe Ansatz (TBA) technique for calculating the finite volume spectrum, we confirm that the observed states are well described by the low energy effective theory of a long string consisting of two translational Goldstone bosons (``phonons"), along with a massive pseudoscalar (``the worldsheet axion") coupled to phonons through a $θ$-term. Moreover, we find that the leading axion-axion and axion-phonon interactions are well approximated by the $T\bar{T}$ deformation of a free axion.
We study worldsheet theory of confining strings in two-dimensional massive adjoint QCD. Similarly to confining strings in higher dimensions this theory exhibits a non-trivial $S$-matrix surviving even in the strict planar limit. In the process of two-particle scattering a zigzag is formed on the worldsheet. It leads to an interesting non-locality and exhibits some properties of a quantum black hole. Ordinarily, identical quantum particles do not carry identity. On the worldsheet they acquire off-shell identity due to strings attached. Identity implies complementarity. We discuss similarities a…
We study restrictions on scattering amplitudes on the worldvolume of branes and strings (such as confining flux tubes in QCD) implied by the target space Poincare symmetry. We focus on exploring the conditions for the string worldsheet theory to be integrable. We prove that for a higher dimensional membrane the scattering amplitudes for the translational Goldstone modes ("branons") are double soft. At one-loop double softness is generically violated for the string worldsheet scattering as a consequence of collinear singularities. Violation of double softness implies in turn the breakdown of in…
Lattice QCD simulations provide crucial information about the worldsheet dynamics of confining strings (flux tubes). An accurate extraction of the worldsheet $S$-matrix from lattice spectra requires accounting for polarization effects. Approximate integrability of the low energy worldsheet theory makes it possible to apply the Thermodynamic Bethe Ansatz to incorporate polarization effects at all orders in the number of windings and at the leading order in the derivative expansion. However, a systematic application of this technique in the presence of non-integrable effects and for multiparticl…
We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to $Q=\sqrt{7\over 16π}\approx 0.37$. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical stri…
Almost massless mesons created at the condensation scale of extra nonabelian gauge group can be candidates of dark energy source. This can be another motivation for introducing an additional confining force.
We present recent results on the spectrum of a confining flux tube that is closed around a spatial torus as a function of its length as well as the spectrum of glueballs. The extraction of the spectra has been realized by simulating four dimensional $SU(N)$ gauge theories and performing measurements using lattice techniques. Regarding flux-tubes, we have performed calculations for $N=3,5,6$ and for various values of spin, parity and longitudinal momentum. Long flux-tubes can be thought of as infinitesimally thin strings; hence their spectrum is expected to be described by an effective string t…
According to the Axionic String Anstaz (ASA) confining flux tubes in pure gluodynamics are in the same equivalence class as a new family of integrable non-critical strings, called axionic strings. In addition to translational modes, axionic strings carry a set of worldsheet axions transforming as an antisymmetric tensor under the group of transverse rotations. We initiate a study of integrable axionic strings at general number of space-time dimensions $D$. We show that in the infinite tension limit worldsheet axions should be described by a peculiar "pseudofree" theory---their $S$-matrix is tr…
Quark confinement is proposed to be a dual Meissner effect of nonAbelian kind. Important hints come from physics of strongly-coupled infrared-fixed-point theories in N=2 supersymmetric QCD, which turn into confining vacua under a small relevant perturbation. The quest for the semiclassical origin of the nonAbelian monopoles, ubiquitous as the infrared degrees of freedom in supersymmetric gauge theories, motivates us to study the quantum dynamics of 2D CP(N-1)model defined on a finite-width worldstrip, with various boundary conditions. The model is found to possess a unique phase ("confinement …
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 \[ b_0={D_{cr}-D_{ph}\over 6}\;. \] Here $b_0=11/3$ is the one-loop $β$-function coefficient in the pure Yang--Mills theory, …
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang--Mills theory both in $D=3$ and $D=4$ space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers…
We study confining strings in massive adjoint two-dimensional chromodynamics. Off-shell, as a consequence of zigzag formation, the resulting worldsheet theory provides a non-trivial dynamical realization of infinite quon statistics. Taking the high energy limit we identify a remarkably simple and novel integrable relativistic $N$-body system. Its symmetry algebra contains an additional "shadow" Poincaré subalgebra. This model describes the $N$-particle subsector of a $T\bar T$-deformed massless fermion.
I review the dark energy solutions by a very light pseudoscalar called "quintessential axion". For the explicit breaking terms, we consider both the global anomaly U(1)$_{\rm global}\times$SU(2)$_W^2$ and the potential $ΔV$. At the field theory level, we will present a strategy for picking up one such pseudoscalar among plenty of pseudoscalars. At string level, numerous antisymmetric tensor fields are pseudoscalars. Including these, we present a confining force example via a $Z_{12-I}$ orbifold compactification of SO(32) heterotic string. In addition, we also aim to draw attention on almost ma…
In this paper we discuss well-known three- and two-dimensional models with confinement, namely, the Polyakov compact electrodynamics in 3D and two-dimensional CP(N-1) sigma model, and reveal changes in the confining regimes of these model upon adding the axion field. In both cases the addition of axion has a drastic impact. In the CP(N-1) model the axion-induced deconfinement was known previously, but we discuss a new feature not considered in the previous publication.
We study meson decays using instanton methods in two string models. The first model is the old string model in flat space which combines strings and massive particles and the second is the holographic, Sakai-Sugimoto model. Using the the old string model, we reproduce the QCD formula for the probability of splitting of the QCD flux tube derived by Casher-Neuberger-Nussinov (CNN). In the holographic model we construct a string worldsheet instanton which interpolates between a single and double string configuration, which determines the decay from one to two dual mesonic particles. The resulting…
Dark gauge sectors and axions are well-motivated in string theory. We demonstrate that if a confining gauge sector gives rise to dark glueballs that are a fraction of the dark matter, and the associated axion has a decay constant near the string scale, then this axion is ultralight and naturally realizes the fuzzy dark matter scenario with a modest tuning of a temperature ratio. Astrophysical observations constrain the size of the glueball component relative to the axionic component, while electric dipole moments constrain mixing with the QCD axion.
We present a major update on the spectrum of the closed flux-tube (torelon) in $D=3+1$ $SU(N)$ gauge theories. Namely, we calculate the excitation spectrum of a confining flux-tube which winds around a spatial torus as a function of its length $l$, for short as well as long tubes. We do so for $N=3,5,6$ and two different values of the lattice spacing. Our states are characterised by the quantum numbers of spin $J$, transverse parity $P_{\perp}$, longitudinal parity $P_{\parallel}$ as well as by the longitudinal momentum $p_{\parallel}$. Our extended basis of operators used in combination with …
In U(1) lattice gauge theory in three spacetime dimensions, the problem of confinement can be studied analytically in a semi-classical approach, in terms of a gas of monopoles with Coulomb-like interactions. In addition, this theory can be mapped to a spin model via an exact duality transformation, which allows one to perform high-precision numerical studies of the confining potential. Taking advantage of these properties, we carried out an accurate investigation of the effective string describing the low-energy properties of flux tubes in this confining gauge theory. We found striking deviati…
