1,720,979 research outputs found
A geometric free field realisation for the genus-two class S theory of type a1
Full text linkWe present a free field realisation for the vertex operator algebra
associated to the genus-two, class superconformal field theory of
type . The free field realisation is in the style of recent
work by the authors, and is formulated in terms of a one-dimensional isotropic
lattice vertex algebra along with two pairs of symplectic fermions. Our
realisation makes manifest an enhanced outer automorphism group
of the VOA that is inherited from the symplectic fermion system. This extends
an outer automorphism that has been observed in recent work of
Kiyoshige and Nishinaka and significantly simplifies the structure of the
algebra. Along the way, we also produce a realisation of the generic subregular
Drinfel'd-Sokolov algebra of type in terms of the
generic principle algebra of type and a
one-dimensional isotropic lattice vertex algebra
Bootstrapping the half-BPS line defect CFT in N=4 supersymmetric Yang-Mills theory at strong coupling
Full text linkWe consider the one-dimensional (1D) conformal field theory defined by the half-BPS Wilson line in planar =4 super Yang-Mills. Using analytic bootstrap methods we derive the four-point function of the superdisplacement operator at fourth order in a strong coupling expansion. Via AdS/CFT, this corresponds to the first three-loop correlator in anti–de Sitter ever computed. To do so we address the operator mixing problem by considering a family of auxiliary correlators. We further extract the anomalous dimension of the lightest nonprotected operator and find agreement with the integrability-based numerical result of Grabner, Gromov, and Julius
Unmixing the Wilson line defect CFT. Part I. Spectrum and kinematics
No full textThis is the first of a series of two papers in which we study the one-dimensional defect CFT defined by insertions of local operators along a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} -BPS Wilson line in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} = 4 super Yang-Mills. In this first paper we focus on the kinematical implications of invariance under the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\mathfrak{o}\mathfrak{s}\mathfrak{p}\left({4}<^>{*}|4\right)\end{document} superconformal algebra preserved by the line. We study correlation functions involving both protected and unprotected supermultiplets and derive the associated superconformal blocks, using two types of superspace for short and long representations. We also discuss the spectrum of defect theories defined by the Wilson line, focusing in particular on fundamental lines in the planar limit: in this case we provide a detailed analysis of the type and number of states both at weak 't Hooft coupling, via the free gauge theory description of the defect CFT, and at strong coupling, where there is a dual description via AdS/CFT. Focusing on the strongly-coupled regime, which will be subject to a detailed analysis using analytic bootstrap techniques in [1], we also develop a strategy that allows to explicitly build superconformal primary operators and their superconformal descendants in terms of the elementary fields in the AdS Lagrangian description. The explicit results will be used in [1] to address the problem of operators mixing at strong coupling. This paper and the companion [1] provide an extended version of the results presented in [2]
Unmixing the Wilson line defect CFT. Part II. Analytic bootstrap
Full text linkIn this second installment of a series of two papers on the -BPS Wilson line defect CFT in = 4 super Yang-Mills, we focus on dynamical aspects of the theory, in particular studying four-point functions with analytic bootstrap methods. Relying on the results of [1] for the kinematics and strong coupling spectrum, we consider various four-point functions in the planar limit, in an expansion for large 't Hooft coupling. Our ultimate goal is to provide a detailed derivation of the four-point function of the displacement supermultiplet at three loops, first presented in [2]. Along the way, we present a large amount of new results including four-point functions with zero, one or two long external supermultiplets. The last two represent a novelty in the analytic bootstrap literature and are instrumental in addressing the problem of operators degeneracy. Such phenomenon leads to the necessity of resolving a mixing problem that is more complicated than those usually encountered in the study of holographic correlators, thus leading us to the development of a new approach that we believe will have a wider range of applicability. Related to this issue, we analyze in some detail the structure of the dilatation operator in this model. Some of the ingredients that we use apply more generally to holographic theories, although a thorough investigation of these aspects is missing, to the best of our knowledge, in most interesting cases
VOAs labelled by complex reflection groups and 4d SCFTs
Full text linkWe define and study a class of N = 2 vertex operator algebras WG labelled by complex reflection groups. They are extensions of the N = 2 super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group G. If G is a Coxeter group, the N = 2 super Virasoro algebra enhances to the (small) N = 4 superconformal algebra. With the exception of G = Z2, which corresponds to just the N = 4 algebra, these are non-deformable VOAs that exist only for a specific negative value of the central charge. We describe a free-field realization of WG in terms of rank(G) βγbc ghost systems, generalizing a construction of Adamovic for the N = 4 algebra at c = −9. If G is a Weyl group, WG is believed to coincide with the N = 4 VOA that arises from the four-dimensional super Yang-Mills theory whose gauge algebra has Weyl group G. More generally, if G is a crystallographic complex reflection group, WG is conjecturally associated to an N = 3 4d superconformal field theory. The free-field realization allows to determine the elusive “R-filtration” of WG, and thus to recover the full Macdonald index of the parent 4d theory
Bootstrapping string dynamics in the 6d theories
Full text linkWe present two complementary approaches to calculating the 2-point function
of stress tensors in the presence of a 1/2 BPS surface defect of the 6d
theories. First, we use analytical bootstrap techniques
at large to obtain the first nontrivial correction to this correlator, from
which we extract the defect CFT (dCFT) data characterising the 2d dCFT of the
1/2 BPS plane. Along the way we derive a supersymmetric inversion formula,
obtain the relevant superconformal blocks and check that crossing symmetry is
satisfied. Notably our result features a holomorphic function whose appearance
is related to the chiral algebra construction of Beem, Rastelli and van Rees.
Second, we use that chiral algebra description to obtain exact results for the
BPS sector of the dCFT, valid at any and for any choice of surface
operator. These results provide a window into the dynamics of strings of the
mysterious 6d theories.Comment: 32 pages, 3 figures; v2: fixed typo in eqn (4.20), minor edits,
published versio
Free Field Realizations from the Higgs Branch
Full text linkWe present free field realizations for the associated vertex operator algebras of a number of four-dimensional = 2 superconformal field theories. Our constructions utilize an exceptionally small set of chiral bosons whose number matches the complex dimensionality of the Higgs branch of the superconformal field theory. In the case of theories whose Higgs branches support additional degrees of freedom (free vector multiplets or decoupled interacting SCFTs), the corresponding “free field realizations” include additional ingredients: symplectic fermions in the case of vector multiplets and a C co-finite VOA in the case of a residual interacting SCFT. The resulting picture is that the associated VOA can be constructed from the Higgs branch effective theory via free field realization. Our constructions also provide a natural realization of the R-filtration of the associated VOA.We present free field realizations for the associated vertex operator algebras of a number of four-dimensional superconformal field theories. Our constructions utilize an exceptionally small set of chiral bosons whose number matches the complex dimensionality of the Higgs branch of the superconformal field theory. In the case of theories whose Higgs branches support additional degrees of freedom (free vector multiplets or decoupled interacting SCFTs), the corresponding "free field realizations" include additional ingredients: symplectic fermions in the case of vector multiplets and a co-finite VOA in the case of a residual interacting SCFT. The resulting picture is that the associated VOA can be constructed from the Higgs branch effective theory via free field realization. Our constructions also provide a natural realization of the -filtration of the associated VOA
VOAs and rank-two instanton SCFTs
Full text linkWe analyze the superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. We further present free field realizations for these algebras in the style of recent work by three of the authors. These realizations transparently reflect the algebraic structure of the Higgs branches of these theories. We find fourth-order linear modular differential equations for the vacuum characters/Schur indices of these theories, which are again uniform across the full family of theories and parameterized by the dual Coxeter number. We comment briefly on expectations for the still higher-rank cases.We analyze the N=2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. We further present free field realizations for these algebras in the style of recent work by three of the authors. These realizations transparently reflect the algebraic structure of the Higgs branches of these theories. We find fourth-order linear modular differential equations for the vacuum characters/Schur indices of these theories, which are again uniform across the full family of theories and parameterized by the dual Coxeter number. We comment briefly on expectations for the still higher-rank cases
New N = 2 superconformal field theories from S -folds
Full text linkWe study the four-dimensional N = 2 superconformal field theories that describe D3-branes probing the recently constructed N = 2 S-folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to S-fold theories via partial Higgsing. We determine several properties of both the S-fold models and this new class of theories, including their central charges, Coulomb branch spectrum, and moduli spaces of vacua, by bringing to bear an array of field-theoretical techniques, to wit, torus-compactifications of six-dimensional N = (1, 0) theories, class S technology, and the SCFT/VOA correspondence
Free field realizations for rank-one SCFTs
Full text linkIn this paper, we construct the associated vertex operator algebras for all N = 2 superconformal field theories of rank one. We give a uniform presentation through free-field realizations, which turns out to be a particularly suitable framework for this task. The elementary building blocks of the construction are dictated by the low energy degrees of freedom on the Higgs branch, which are well understood for rank-one theories. We further analyze the interplay between Higgs and Coulomb data on the moduli space of vacua, which tightly constrain the overall structure of the free field realizations. Our results suggest a plausible bottom-up classification scheme for low-rank SCFTs incorporating vertex algebra techniques
- …
