Dual Superconductor Model of Confinement: Quantum-String Representation of the 4D Yang–Mills Theory on a Torus and the Correlation Length away from the London Limit

This paper is devoted to the dual superconductor model of confinement in the 4D Yang–Mills theory. In the first part, we consider the latter theory compactified on a torus, and use the dual superconductor model in order to obtain the Polchinski–Strominger term in the string representation of a Wilson loop. For a certain realistic critical value of the product of circumferences of the compactification circles, which is expressed in terms of the gluon condensate and the vacuum correlation length, the coupling of the Polchinski–Strominger term turns out to be such that the string conformal anomaly cancels out, making the string representation fully quantum. In the second part, we use the analogy between the London limit of the dual superconductor and the low-energy limit of the 4D compact QED, to obtain the partition function of the dual superconductor model away from the London limit. There, we find a decrease of the vacuum correlation length, and derive the corresponding potential of monopole currents.

Spontaneously broken boosts in CFTs

Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as O(1). We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.

De Sitter entropy as holographic entanglement entropy

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

The conformal anomaly action to fourth order (4T) in $$d=4$$ in momentum space

We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations (h) of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to $$R\square ^{-1}$$ R □ - 1 interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.

$$ T\overline{T} $$ Deformation of stress-tensor correlators from random geometry

We study stress-tensor correlators in the $$ T\overline{T} $$ T T ¯ -deformed conformal field theories in two dimensions. Using the random geometry approach to the $$ T\overline{T} $$ T T ¯ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $$ T\overline{T} $$ T T ¯ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $$ T\overline{T} $$ T T ¯ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check consistency with the $$ T\overline{T} $$ T T ¯ -deformed operator product expansions of the stress tensor. A salient feature of the $$ T\overline{T} $$ T T ¯ -deformed stress-tensor correlators is a logarithmic correction that is absent in two and three-point functions but starts appearing in a four-point function.

The conformal anomaly and anomaly-induced action

This chapter describes in detail basic results concerning the conformal (trace) anomaly and anomaly-induced action in four spacetime dimensions. It is shown how the anomaly appears from the non-local form factors discussed in chapter 16. Starting from the conformal transformations, the necessary invariants and transformation rules are obtained. The simplest derivation of the anomaly in dimensional regularization is explained, followed by the equally simple calculation of the anomaly-induced effective action of gravity. The chapter also briefly discusses applications of the induced effective action in cosmology and black hole physics.