conformal bootstrap
Recently Published Documents


TOTAL DOCUMENTS

116
(FIVE YEARS 53)

H-INDEX

24
(FIVE YEARS 5)

2022 ◽  
Vol 105 (2) ◽  
Author(s):  
Andrea Cavaglià ◽  
Nikolay Gromov ◽  
Julius Julius ◽  
Michelangelo Preti

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Yin-Chen He ◽  
Junchen Rong ◽  
Ning Su

We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions d>2d>2. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of decoupling operator, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of 2d2d Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a U(1)U(1) gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both d=3d=3 and d=2+\epsilond=2+ϵ dimensions.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
António Antunes ◽  
Miguel S. Costa ◽  
João Penedones ◽  
Aaditya Salgarkar ◽  
Balt C. van Rees

Abstract The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS2, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Ferdinando Gliozzi ◽  
Pedro Liendo ◽  
Marco Meineri ◽  
Antonio Rago
Keyword(s):  

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Nikita Nemkov ◽  
Sylvain Ribault

We revisit the critical two-dimensional Ashkin–Teller model, i.e. the \mathbb{Z}_2ℤ2 orbifold of the compactified free boson CFT at c=1c=1. We solve the model on the plane by computing its three-point structure constants and proving crossing symmetry of four-point correlation functions. We do this not only for affine primary fields, but also for Virasoro primary fields, i.e. higher twist fields and degenerate fields. This leads us to clarify the analytic properties of Virasoro conformal blocks and fusion kernels at c=1c=1. We show that blocks with a degenerate channel field should be computed by taking limits in the central charge, rather than in the conformal dimension. In particular, Al. Zamolodchikov’s simple explicit expression for the blocks that appear in four-twist correlation functions is only valid in the non-degenerate case: degenerate blocks, starting with the identity block, are more complicated generalized theta functions.


2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Simon Caron-Huot ◽  
Dalimil Mazáč ◽  
Leonardo Rastelli ◽  
David Simmons-Duffin

Abstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.


2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Chi-Ming Chang ◽  
Sean Colin-Ellerin ◽  
Cheng Peng ◽  
Mukund Rangamani

Abstract We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $$ \mathcal{N} $$ N = 2 large N Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large N spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.


2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
António Antunes

Abstract We propose a bootstrap program for CFTs near intersecting boundaries which form a co-dimension 2 edge. We describe the kinematical setup and show that bulk 1-pt functions and bulk-edge 2-pt functions depend on a non-trivial cross-ratio and on the angle between the boundaries. Using the boundary OPE (BOE) with respect to each boundary, we derive two independent conformal block expansions for these correlators. The matching of the two BOE expansions leads to a crossing equation. We analytically solve this equation in several simple cases, notably for a free bulk field, where we recover Feynman-diagrammatic results by Cardy.


2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marten Reehorst ◽  
Slava Rychkov ◽  
David Simmons-Duffin ◽  
Benoit Sirois ◽  
Ning Su ◽  
...  

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.


Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 348
Author(s):  
Silvia Penati

We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.


Sign in / Sign up

Export Citation Format

Share Document