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Results for “Superconformal algebras”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Partial spectral flow in the D1D5 CFT

The two-dimensional 𝒩 = 4 superconformal algebra has a free field realization with four bosons and four fermions. There is an automorphism of the algebra called spectral flow. Under spectral flow, the four fermions are transformed together. In this paper, we study partial spectral flow where only two of the four fermions are transformed. Partial spectral flow is applied to the D1D5 CFT where a marginal deformation moves the CFT away from the free point. The partial spectral flow is broken by the deformation. We show that this effect can be studied due to a transformation of the deformation which is well-defined under partial spectral flow. As a result in the spectrum, we demonstrate how to compute the second-order energy lift of a D1D5P state through its partial spectral flowed state. We find that D1D5P states related by partial spectral flow do not have the same lift in general.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Moonshine, superconformal symmetry, and quantum error correction

Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a c = 24 twodimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway symmetry group of a c = 12 CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu group M24 has led to the study of K3 sigma models with large symmetry groups. A particular K3 CFT with a maximal symmetry group preserving (4, 4) superconformal symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland [41]. The present paper shows that in both the GTVW and c = 12 theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism groups of these codes lift to symmetry groups in the CFT preserving the superconformal generators. In the case of the N = 1 supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the symmetry group is the maximal subgroup of M24 known as the sextet group. (The sextet group is also known as the holomorph of the hexacode.) Building on [41] the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a group of symmetries of RR states. Moreover, (4, 1) superconformal symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the N = 4 superconformal algebra. The symmetry group preserving (4, 1) is larger than that preserving (4, 4).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Nonrenormalization theorem for $\mathcal{N}$ = (4, 4) interface entropy

We derive a formula for the half-BPS interface entropy between any pair of $\mathcal{N}$ = (4, 4) theories on the same conformal manifold. This generalizes the diastasis formula derived in [1] for $\mathcal{N}$ = (2, 2) theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of $\mathcal{N}$ = (2, 2) supersymmetry. To derive the $\mathcal{N}$ = (4, 4) formula, we use the fact that the conformal manifold of $\mathcal{N}$ = (4, 4) theories is symmetric and quaternionic-Kähler and that its isotropy group contains the SU(2) ⊗ SU(2) external automorphism of the $\mathcal{N}$ = (4, 4) superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in [2] that the interface entropy for half-BPS Janus solutions in type IIB supergravity on AdS 3 × S 3 × T 4 coincides with the corresponding quantity in their free conformal field limits.

AdS-CFT correspondence↗
DOE OSTI2021

\( \mathcal{N} \) = 2 supersymmetric partially massless fields and other exotic non-unitary superconformal representations

We find and classify the simplest \( \mathcal{N} \) = 2 SUSY multiplets on AdS 4 which contain partially massless fields. We do this by studying representations of the \( \mathcal{N} \) = 2, d = 3 superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the \( \mathcal{N} \) = 1 case, the simplest \( \mathcal{N} \) = 2 multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that \( \mathcal{N} \) = 2 supersymmetry allows for short multiplets that contain partially massless spin- s particles of depth t = s – 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Vertex algebra of extended operators in 4d N=2 superconformal field theories. Part I

Abstract We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d$$ \mathcal{N} $$ N =2 SCFTs. The extended operators are constructed from the local operators in this cohomology — the Schur operators — by a version of topological descent. They are line, surface, and domain wall world volume integrals of certain super descendants of Schur operators. Their world volumes extend in directions transverse to a spatial plane in Minkowski space-time. As operators in the cohomology of these twisted Schur supercharges, their correlators are (locally) meromorphic functions only of the positions where they intersect this plane. This implies the extended operators enlarge the vertex operator algebra of the Schur operators. We illustrate this enlarged vertex algebra by computing some extended-operator product expansions within a subalgebra of it for the free hypermultiplet SCFT.

Physics↗
DOE OSTI2020

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

From large to small $$ \mathcal{N} $$ = (4, 4) superconformal surface defects in holographic 6d SCFTs

Abstract Two-dimensional (2d)$$ \mathcal{N} $$ N = (4, 4) Lie superalgebras can be either “small” or “large”, meaning their R-symmetry is either$$ \mathfrak{so} $$ so (4) or$$ \mathfrak{so} $$ so (4) ⊕$$ \mathfrak{so} $$ so (4), respectively. Both cases admit a superconformal extension and fit into the one-parameter family$$ \mathfrak{d} $$ d (2,1;γ) ⊕$$ \mathfrak{d} $$ d (2,1;γ), with parameterγ∈ (−∞,∞). The large algebra corresponds to generic values ofγ, while the small case corresponds to a degeneration limit withγ→ −∞. In 11d supergravity, we study known solutions with superisometry algebra$$ \mathfrak{d} $$ d (2,1;γ) ⊕$$ \mathfrak{d} $$ d (2,1;γ) that are asymptotically locally AdS 7 ×𝕊 4 . These solutions are holographically dual to the 6d maximally superconformal field theory with 2d superconformal defects invariant under$$ \mathfrak{d} $$ d (2,1;γ) ⊕$$ \mathfrak{d} $$ d (2,1;γ). We show that a limit of these solutions, in whichγ→ −∞, reproduces another known class of solutions, holographically dual tosmall$$ \mathcal{N} $$ N = (4, 4) superconformal defects. We then use this limit to generate new small$$ \mathcal{N} $$ N = (4, 4) solutions with finite Ricci scalar, in contrast to the known small$$ \mathcal{N} $$ N = (4, 4) solutions. We then use holography to compute the entanglement entropy of a spherical region centered on these small$$ \mathcal{N} $$ N = (4, 4) defects, which provides a linear combination of defect Weyl anomaly coefficients that characterizes the number of defect-localized degrees of freedom. We also comment on the generalization of our results to include$$ \mathcal{N} $$ N = (0,4) surface defects through orbifolding.

Physics↗
DOE OSTI2021

Fun with F24

We study some special features of F 24 , the holomorphic c = 12 superconformal field theory (SCFT) given by 24 chiral free fermions. We construct eight different Lie superalgebras of “physical” states of a chiral superstring compactified on F 24 , and we prove that they all have the structure of Borcherds-Kac-Moody superalgebras. This produces a family of new examples of such superalgebras. The models depend on the choice of an \( \mathcal{N} \) = 1 supercurrent on F 24 , with the admissible choices labeled by the semisimple Lie algebras of dimension 24. We also discuss how F 24 , with any such choice of supercurrent, can be obtained via orbifolding from another distinguished c = 12 holomorphic SCFT, the \( \mathcal{N} \) = 1 supersymmetric version of the chiral CFT based on the E 8 lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Twisted circle compactifications of 6 d SCFTs

We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗