Ferdinando Gliozzi

Constraints on conformal field theories in diverse dimensions from the bootstrap mechanism.

Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It appears that the calculations can be done only for theories lying at the boundary of the allowed parameter space. Here it is pointed out that a similar method can be applied to a larger class of CFT’s, whether unitary or not, and no free parameter remains, provided we know the fusion algebra of the low lying primary operators. As an example we calculate using first principles, with no phenomenological input, the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity in three and four space dimensions. The edge exponents compare favorably with the latest numerical estimates. A consistency check of this approach on the 3d critical Ising model is also made.

Critical exponents of the 3d Ising and related models from conformal bootstrap

A bstractThe constraints of conformal bootstrap are applied to investigate a set of conformal field theories in various dimensions. The prescriptions can be applied to both unitary and non unitary theories allowing for the study of the spectrum of low-lying primary operators of the theory. We evaluate the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity for 2 ≤ D ≤ 6. Likewise we obtain the scaling dimensions of six scalars and four spinning operators for the 3d critical Ising model. Our findings are in agreement with existing results to a per mill precision and estimate several new exponents.

String effects in the Wilson loop: A High precision numerical test

Abstract We test numerically the effective string description of the infrared limit of lattice gauge theories in the confining regime. We consider the 3D Z 2 lattice gauge theory, and we define ratios of Wilson loops such that the predictions of the effective string theory do not contain any adjustable parameters. In this way we are able to obtain a degree of accuracy high enough to show unambiguously that the flux-tube fluctuations are described, in the infrared limit, by an effective bosonic string theory.

Boundary and Interface CFTs from the Conformal Bootstrap

A bstractWe explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N ) models through numerical solutions to the crossing equations with the method of determinants. In the extraordinary transition, where the low-lying spectrum of the surface operators is known, we use the bootstrap equations to obtain information on the bulk spectrum of the theory. In the ordinary transition the knowledge of the low-lying bulk spectrum allows to calculate the scale dimension of the relevant surface operator, which compares well with known results of two-loop calculations in 3d. Estimates of various OPE coefficients are also obtained. We also analyze in 4-ϵ dimensions the renormalization group interface between the O(N ) model and the free theory and check numerically the results in 3d.

Spinor algebra of the one-component lattice fermions

Abstract We develop a general formalism to translate the Susskind one-component theory of free fermions in a formulation with conventional Dirac spinors. It results that Susskind theory has parity-violating and flavour-changing terms which vanish only in the continuum limit. Gauge fields destroy the equivalence between the one-component and the conventional formulations. In particular the one-component fermions respond to a gauge field as they were in a curved space-time. However, this gravity effect vanishes if one takes a naive continuum limit.

Entanglement entropy and twist fields

The entanglement entropy of a subsystem A of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as the vacuum expectation value of a suitable observable in a system made with n independent copies of the original system. We use this property to numerically evaluate it in some two-dimensional critical systems, where it can be compared with the results of Calabrese and Cardy, who wrote the same quantity in terms of correlation functions of twist fields of a conformal field theory. Although the two calculations match perfectly even in finite systems when the system A consists of a single interval, they disagree whenever the subsystem A is composed of more than one connected part. The reasons of this disagreement are explained.

Unified dual model for interacting open and closed strings

We construct the vertices which describe the emission of closed string particles (pomerons) out of open string states (reggeons). Using those vertices we can construct a ghost-free unified dual model for the amplitude of an arbitrary number of reggeons and pomerons which contains both the conventional Veneziano model and the Shapiro- Virasoro model. The factorization properties of this model are studied in detail. In particular, we extract the reggeon-pomeron direct coupling from the channels where both reggeons and pomerons can be exchanged.

Width of the confining string in Yang-Mills theory.

We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.

ADE functional dilogarithm identities and integrable models

We describe a new infinite family of multi-parameter functional equations for the Rogers dilogarithm, generalizing Abels and Eulers formulas. They are suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization Group flow of 2D integrable, ADE-related quantum field theories. The known sum rules for the central charge of critical fixed points can be obtained as special cases of these. We conjecture that similar functional identities can be constructed for any rational integrable quantum field theory with factorized S-matrix and support it with extensive numerical checks.Abstract We describe a new infinite family of multi-parameter functional equations for the Rogers dilogarithm, generalizing Abels and Eulers formulas. They are suggested by the Thermodynamic Bethe Ansatz approach to the renormalization group flow of 2D integrable, ADE-related quantum field theories. The known sum rules for the central charge of critical fixed points can be obtained as special cases of these. We conjecture that similar functional identities can be constructed for any rational integrable quantum field theory with factorized S -matrix and support it with extensive numerical checks.

Line defects in the 3d Ising model

A bstractWe investigate the properties of the twist line defect in the critical 3d Ising model using Monte Carlo simulations. In this model the twist line defect is the boundary of a surface of frustrated links or, in a dual description, the Wilson line of the