Superconformal Symmetry Research Articles

Three-point functions of higher-spin supercurrents in 4D N=1 SCFT: General formalism for arbitrary superspins

We analyze the general structure of the three-point functions involving conserved higher-spin “vectorlike” supercurrents Js(z)≔Jα(s)α˙(s)(z) in four-dimensional N=1 superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilize a computational approach to analyze the general structure of the three-point function ⟨Js1(z1)Js2′(z2)Js3′′(z3)⟩ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to 2 min(si)+2 independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion. Published by the American Physical Society 2024

Superconformal monodromy defects in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}=4 SYM and LS theory

We study type IIB supergravity solutions that are dual to two-dimensional superconformal defects in d = 4 SCFTs which preserve N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (0, 2) supersymmetry. We consider solutions dual to defects in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM theory that have non-trivial monodromy for U(1)3 ⊂ SO(6) global symmetry and we also allow for the possibility of conical singularities. In addition, we consider the addition of fermionic and bosonic mass terms that have non trivial dependence on the spatial directions transverse to the defect, while preserving the superconformal symmetry of the defect. We compute various physical quantities including the central charges of the defect expressed as a function of the monodromy, the on-shell action as well as associated supersymmetric Rényi entropies. Analogous computations are carried out for superconformal defects in the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, d = 4 Leigh-Strassler SCFT. We also show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow.

N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal higher-spin multiplets and their hypermultiplet couplings

We construct an off-shell N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin s gauge N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supermultiplet in a general N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 conformal supergravity background. We heavily use N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2, 4D harmonic superspace that provides an unconstrained superfield Lagrangian description. We start with N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 global superconformal symmetry transformations of the free hypermultiplet model and require invariance of the cubic vertices of general form under these transformations and their gauged version. As a result, we deduce N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2, 4D unconstrained analytic superconformal gauge potentials for an arbitrary integer s. These are the basic ingredients of the approach under consideration. We describe the properties of the gauge potentials, derive the corresponding superconformal and gauge transformation laws, and inspect the off-shell contents of the thus obtained N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal higher-spin s multiplets in the Wess-Zumino gauges. The spin s multiplet involves 8(2s− 1)B + 8(2s− 1)F essential off-shell degrees of freedom. The cubic vertex has the generic structure higher spin gauge superfields × hypermultiplet supercurrents. We present the explicit form of the relevant supercurrents.

Topological defects in K3 sigma models

We consider the topological defect lines commuting with the spectral flow and the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (4, 4) superconformal symmetry in two dimensional non-linear sigma models on K3. By studying their fusion with boundary states, we derive a number of general results for the category of such defects. We argue that while for certain K3 models infinitely many simple defects, and even a continuum, can occur, at generic points in the moduli space the category is actually trivial, i.e. it is generated by the identity defect. Furthermore, we show that if a K3 model is at the attractor point for some BPS configuration of D-branes, then all topological defects have integral quantum dimension. We also conjecture that a continuum of topological defects arises if and only if the K3 model is a (possibly generalized) orbifold of a torus model. Finally, we test our general results in a couple of examples, where we provide a partial classification of the topological defects.

Quantum [formula omitted]-Yang-Mills from the IKKT matrix model

We study the one-loop effective action of the higher-spin gauge theory induced by the IKKT matrix model on a M1,3×K background, where M1,3 is an FLRW cosmological spacetime brane and K are compact fuzzy extra dimensions. In particular, we show that all non-abelian (hs-valued) gauge fields in this model acquire mass via quantum effects, thus avoiding no-go theorems. This leads to a massive non-abelian quantum hs-Yang-Mills theory, whose detailed structure depends on K. The stabilization of K at one loop is understood as a result of the coupling between K and the U(1)-flux bundle on space-time. This flux stabilization induces the KK scale into the N=4 SYM sector of the model, which break superconformal symmetry.

Color symmetry and confinement as an underlying superconformal structure in holographic QCD

Dedicated to the memory of our colleague, Harald Fritzsch, who, together with Murray Gell-Mann, introduced the color quantum number as the exact symmetry responsible for the strong interaction, thus establishing quantum chromodynamics (QCD) as a fundamental non-Abelian gauge theory. A basic understanding of hadron properties, however, such as confinement and the emergence of a mass scale, from first principles QCD has remained elusive: Hadronic characteristics are not explicit properties of the QCD Lagrangian and perturbative QCD, so successful in the large transverse momentum domain, is not applicable at large distances. In this article, we shall examine how this daunting obstacle is overcome in holographic QCD with the introduction of a superconformal symmetry in anti de Sitter (AdS) space which is responsible for confinement and the introduction of a mass scale within the superconformal group. When mapped to light-front coordinates in physical spacetime, this approach incorporates supersymmetric relations between the Regge trajectories of meson, baryon and tetraquark states which can be visualized in terms of specific [Formula: see text] color representations of quarks. We will also briefly discuss here the implications of holographic models for QCD color transparency in view of the present experimental interest.

Defect two-point functions in 6D (2,0) theories

We consider correlation functions in 6D (2,0) theories of two 12-Bogomol’nyi-Prasad-Sommerfield (BPS) operators inserted away from a 12-BPS surface defect. In the large central-charge limit the leading connected contribution corresponds to sums of tree-level Witten diagram in AdS7×S4 in the presence of an AdS3 defect. We show that these correlators can be uniquely determined by imposing only superconformal symmetry and consistency conditions, eschewing the details of the complicated effective Lagrangian. We explicitly compute all such two-point functions. The result exhibits remarkable hidden simplicity. Published by the American Physical Society 2024

Bootstrapping the effect of the twist operator in the D1D5 CFT

In the D1D5 CFT the twist operator of order 2 can twist together two copies in the untwisted sector into a single joined copy in the twisted sector. Traditionally, this effect is computed by using the covering map method. Recently, a new method was developed using the Bogoliubov ansatz and conformal symmetry to compute this effect in a toy model of one free boson. In this paper, we use this method with superconformal symmetry to compute the effect of the twist operator in the D1D5 CFT. This may provide more effective tools for computing correlation functions of twist operators in this system.

Self duality in unconventional conformal supersymmetry

In this work, we study (anti-)self duality conditions in unconventional conformal supersymmetry. We focus on a theory constructed in a Townsend-MacDowell-Mansouri form for an SU(2, 2|N) gauge connection with matter fields in the adjoint representation. We find bosonic solutions that correspond to analytic gravitational instantons with nontrivial torsion. These configurations can be regarded as the torsional generalization of the Taub-NUT/Bolt-AdS and Eguchi-Hanson metric and they are (anti-)self-dual with respect to a generalized dual operator. We explore their global properties and show that they saturate a BPS bound.

Algebro-geometrical orientifold and IR dualities

Orientifold projections are an important ingredient in the geometrical engineering of Quantum Field Theory. However, an orientifold can break down the superconformal symmetry and no new superconformal fixed points are admitted (scenario II); nevertheless, in some cases, dubbed scenarios I and III orientifold, a new IR fixed point is achieved and, for scenario III examples, some still not fully understood IR duality seems to emerge. Here we give an algebro-geometrical point of view of orientifold for toric varieties and we propose the existence of relevant operators that deform the starting oriented Conformal Field Theory triggering a flow. We briefly discuss a possible holographic description of this flow.

Emergent Strings at an Infinite Distance with Broken Supersymmetry

We investigate the infinite-distance properties of families of unstable flux vacua in string theory with broken supersymmetry. To this end, we employ a generalized notion of distance in the moduli space and we build a holographic description for the non-perturbative regime of the tunneling cascade in terms of a renormalization group flow. In one limit, we recover an exponentially-light tower of Kaluza-Klein states, while in the opposite limit, we find a tower of higher-spin excitations of D1-branes, realizing the emergent string proposal. In particular, the holographic description includes a free sector, whose emergent superconformal symmetry resonates with supersymmetric stability, the CFT distance conjecture and S-duality. We compute the anomalous dimensions of scalar vertex operators and single-trace higher-spin currents, finding an exponential suppression with the distance which is not generic from the renormalization group perspective, but appears specific to our settings.

N = (2, 0) AdS3 solutions of M-theory

We consider the most general solutions of eleven-dimensional supergravity preserving N = 2 supersymmetry whose metrics are warped products of three-dimensional anti-de Sitter space with an eight-dimensional manifold, focusing on those realising (2,0) superconformal symmetry. We give a set of necessary and sufficient conditions for a solution to be supersymmetric, which can be phrased, in the general case, in terms of a local SU(2) structure and its intrinsic torsion. We show that these supergravity backgrounds always admit a nowhere-vanishing Killing vector field that preserves the solution and encodes the U(1) R-symmetry of the dual field theory. We illustrate our results with examples which have appeared in the literature, including those with SU(4), G2 and SU(3) structures, and discuss new classes of Minkowski solutions.

Conformal Interactions Between Matter and Higher‐Spin (Super)Fields

AbstractIn even spacetime dimensions, the interacting bosonic conformal higher‐spin (CHS) theory can be realised as an induced action. The main ingredient in this definition is the model describing a complex scalar field φ coupled to an infinite set of background CHS fields h, with possessing a non‐abelian gauge symmetry. Two characteristic features of the perturbative constructions of given in the literature are: (i) the background spacetime is flat; and (ii) conformal invariance is not manifest. In the present paper we provide a new derivation of this action in four dimensions such that (i) is defined on an arbitrary conformally‐flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the supersymmetric case. Specifically, we construct, for the first time, a model for a conformal scalar/chiral multiplet Φ coupled to an infinite set of background higher‐spin superfields H. Our action possesses a non‐abelian gauge symmetry which naturally generalises the linearised gauge transformations of conformal half‐integer superspin multiplets. The other fundamental features of this model are: (i) is defined on an arbitrary conformally‐flat superspace background; and (ii) the background superconformal symmetry is manifest. Making use of , an interacting superconformal higher‐spin theory can be defined as an induced action.

Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

AbstractWe develop a general formalism to study the three‐point correlation functions of conserved higher‐spin supercurrent multiplets in 4D superconformal theory. All the constraints imposed by superconformal symmetry on the three‐point function are systematically derived for arbitrary , thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in , where is the supercurrent. We find that this three‐point function depends on two independent tensor structures, though the precise form of the correlator depends on whether r is even or odd. The case reproduces the three‐point function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form and , where L is the flavour current multiplet.

Celestial dual superconformal symmetry, MHV amplitudes and differential equations

Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the Mellin transform. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of mathcal{N} = 4 Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial n-point tree-level MHV amplitudes and identify their momentum space origins.

Non-relativistic ten-dimensional minimal supergravity

We construct a non-relativistic limit of ten-dimensional mathcal{N} = 1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called ‘self-dual’ Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action.

Three-point functions of higher-spin spinor current multiplets in mathcal{N} = 1 superconformal theory

In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1…αk) of arbitrary rank in four-dimensional mathcal{N} = 1 superconformal theory. We find that the correlation function of three such operators leftlangle {overline{S}}_{dot{alpha}(k)}left({z}_1right){S}_{beta left(k+lright)}left({z}_2right){overline{S}}_{dot{gamma}(l)}left({z}_3right)rightrangle is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l. In addition, we present the general structure of mixed correlators of the form leftlangle {overline{S}}_{dot{alpha}(k)}left({z}_1right){S}_{alpha (k)}left({z}_2right)Lleft({z}_3right)rightrangle and leftlangle {overline{S}}_{dot{alpha}(k)}left({z}_1right){S}_{alpha (k)}left({z}_2right){J}_{gamma dot{gamma}}left({z}_3right)rightrangle , where L is the flavour current multiplet and {J}_{gamma dot{gamma}} is the supercurrent.

Closed string deformations in open string field theory. Part III. mathcal{N} = 2 worldsheet localization

In this paper, which is the last of a series including [1, 2] we first verify that the two open-closed effective potentials derived in the previous paper from the WZW theory in the large Hilbert space and the A∞ theory in the small Hilbert space have the same vacuum structure. In particular, we show that mass-term deformations given by the effective (open)2-closed couplings are the same, provided the effective tadpole is vanishing to first order in the closed string deformation. We show that this condition is always realized when the worldsheet BCFT enjoys a global mathcal{N} = 2 superconformal symmetry and the deforming closed string belongs to the chiral ring in both the holomorphic and anti-holomorphic sector. In this case it is possible to explicitly evaluate the mass deformation by localizing the SFT Feynman diagrams to the boundary of world-sheet moduli space, reducing the amplitude to a simple open string two-point function. As a non-trivial check of our construction we couple a constant Kalb-Ramond closed string state to the OSFT on the D3–D(−1) system and we show that half of the bosonic blowing-up moduli become tachyonic, making the system condense to a bound state whose binding energy we compute exactly to second order in the closed string deformation, finding agreement with the literature.

Celestial superamplitude in mathcal{N} = 4 SYM theory

Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in mathcal{N} = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of mathcal{N} = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied mathcal{N} = 4 SYM amplitudes via 2D celestial conformal field theory.

Color transparency and the proton form factor: Evidence for the Feynman mechanism

A recent experiment [{\bf Phys. Rev. Lett. 126,082301 (2021)}] used the $(e,e'p)$ reaction on $^{12}$C to search for the effects of color transparency (the absence of final state interactions). Color transparency was said to be ruled out. The ability to observe the effects of color transparency depends on the ability of a putative point-like-configuration (PLC), formed in a high-momentum transfer coherent reaction, to escape the nucleus without expanding its size. We study the expansion aspect of color transparency using superconformal baryon-meson symmetry and light-front holographic QCD. A new formalism is obtained and used to analyze the recent experiment. The resulting conclusion is that effects of expansion would not be sufficiently significant in causing final state interactions to occur. Therefore we conclude that a PLC was not formed. This means that the Feynman mechanism involving virtual photon absorption on a single high momentum quark is responsible for high momentum electromagnetic form factor of the proton.