Spectral determinants for twist field correlators

Abstract

Twist fields were introduced a few decades ago as a quantum counterpart to classical kink configurations and disorder variables in low dimensional field theories. In recent years they received a new incarnation within the framework of geometric entropy and strong coupling limit of four-dimensional scattering amplitudes. In this paper, we study their two-point correlation functions in a free massless scalar theory, namely, twist--twist and twist--anti-twist correlators. In spite of the simplicity of the model in question, the properties of the latter are far from being trivial. The problem is reduced, within the formalism of the path integral, to the study of spectral determinants on surfaces with conical points, which are then computed exactly making use of the zeta function regularization. We also provide an insight into twist correlators for a massive complex scalar by means of the Lifshitz-Krein trace formula.

21 pages, 2 figures

References in corpus (15)

• Gluon scattering amplitudes at strong coupling
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Comments on operators with large spin
• Functional Determinants in Quantum Field Theory
• On the collinear limit of scattering amplitudes at strong coupling
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• Lambert series and q-functions near q=1
• Expectation values of twist fields and universal entanglement saturation of the free massive boson
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes
• Nonperturbative enhancement of superloop at strong coupling
• Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians
• Vacuum expectation value of twist fields
• Twisting perturbed parafermions
• Moduli spaces of meromorphic functions and determinant of Laplacian
• Scattering om two Aharonov-Bohm vortices

Cited by in corpus (3)

• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM