Minimal unitary representation of 5d superconformal algebra F(4) and AdS6/CFT5 higher spin (super)-algebras by Sudarshan Fernando, Murat Günaydin

“…These results are then extended to the construction of the unique higher spin AdS6/CFT5 superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.…”
Get full text

Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results by Adamovic, Drazen, Kac, Victor, Frajria, Pierluigi Moseneder, Papi, Paolo, Perse, Ozren

“…We find all values of k∈C, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra Wk(g,θ) is conformal, where g is a basic simple Lie superalgebra and −θ its minimal root. In particular, it turns out that if Wk(g,θ) does not collapse to its affine part, then the possible values of these k are either −[Formula presented], where h∨ is the dual Coxeter number of g for the normalization (θ,θ)=2. …”
Get full text

Gaudin model and Deligne’s category by Feigin, B., Rybnikov, L., Uvarov, F.

“…Motivated by the Bethe ansatz conjecture for the Gaudin model associated with the Lie superalgebra $$\mathfrak {gl}_{n\vert n'}$$ gl n | n ′ , we show that a ratio of monodromy-free differential operators is a pseudo-differential operator without monodromy.…”
Get full text

On the critical behaviour of the integrable q-deformed OSp(3|2) superspin chain by Holger Frahm, Konstantin Hobuß, Márcio J. Martins

“…This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the OSp(3|2) superalgebra. The finite-size properties of the eigenspectra are computed by solving the respective Bethe ansatz equations for large system sizes allowing us to uncover the low-lying critical exponents. …”
Get full text

A positive energy theorem for AdS solitons by Andrés Anabalon, Mattia Cesàro, Antonio Gallerati, Alfredo Giambrone, Mario Trigiante

“…By constructing the asymptotic superalgebra, we establish a positive energy theorem for the magnetic AdS4 solitons admitting well-defined asymptotic Killing spinors, antiperiodic on a contractible S1. …”
Get full text

Warped AdS6 × S 2 in Type IIB supergravity II: global solutions and five-brane webs by Eric D’Hoker, Michael Gutperle, Christoph F. Uhlemann

“…Abstract Motivated by the construction of holographic duals to five-dimensional superconformal quantum field theories, we obtain global solutions to Type IIB supergravity invariant under the superalgebra F (4) on a space-time of the form AdS6 × S 2 warped over a two-dimensional Riemann surface Σ. …”
Get full text

Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology by Felix M. Haehl, R. Loganayagam, Mukund Rangamani

“…These can be understood rather simply as the consequence of a topological (BRST) algebra, called the universal Schwinger-Keldysh superalgebra, as explained in our compan-ion paper [1]. …”
Get full text

Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories by Igor Bandos

“…We also discuss some relevant representations of the M-theory superalgebra which, in the present context, describes supersymmetry of the 11D EFT.…”
Get full text

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$ Z2×Z2 -graded mechanics: the classical theory by N. Aizawa, Z. Kuznetsova, F. Toppan

“…Classical actions invariant under the $${{\mathbb {Z}}}_2\times {\mathbb {Z}}_2$$ Z2×Z2 -graded superalgebra are constructed for both single multiplets and interacting multiplets. …”
Get full text

Supersymmetric localization in AdS5 and the protected chiral algebra by Federico Bonetti, Leonardo Rastelli

“…We propose that the large N limit of the chiral algebra of N=4 $$ \mathcal{N}=4 $$ SYM is again dual to Chern-Simons theory, with gauge algebra a suitable higher-spin superalgebra.…”
Get full text

Three-dimensional hypergravity theories and semigroup expansion method by Ricardo Caroca, Patrick Concha, Javier Matulich, Evelyn Rodríguez, David Tempo

“…First, by expanding the osp $$ \mathfrak{osp} $$ (1|4) superalgebra with a particular semigroup a generalized hyper-Poincaré algebra is found. …”
Get full text

Fluxes, twisted tori, monodromy and U(1) supermembranes by M. P. Garcia del Moral, C. Las Heras, P. Leon, J. M. Pena, A. Restuccia

“…The nonzero mode algebra corresponds to a massive superalgebra that preserves either 1/2 or 1/4 of the original supersymmetry depending on the state considered.…”
Get full text

Path Integral Methods for Single Band Hubbard Model by N. Heydari, S. Azakov

“…In this case one should use generalized coherent states for superalgebra in order to get a path integral formulation. …”
Get full text

Classification of Degenerate Verma Modules for E(5, 10) by Cantarini, Nicoletta, Caselli, Fabrizio, Kac, Victor

“…In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}=E(5,10)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>10</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> with the subalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}_{\ge 0}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> of minimal codimension. …”
Get full text

BPS Wilson loops in N $$ \mathcal{N} $$ ≥ 2 superconformal Chern-Simons-matter theories by Andrea Mauri, Hao Ouyang, Silvia Penati, Jun-Bao Wu, Jiaju Zhang

“…Moreover, if the quiver contains triangles, it cannot be interpreted as a super-matrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in N $$ \mathcal{N} $$ = 4 orbifold ABJM theory. …”
Get full text

New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models by Naruhiko Aizawa, Ren Ito, Zhanna Kuznetsova, Francesco Toppan

“…By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained.The graded superspace calculus of the Z2×Z2-graded worldline super-Poincaré algebra induces two-dimensional Z2×Z2-graded relativistic models; they are invariant under a new Z2×Z2-graded 2D super-Poincaré algebra which differs from the previous two Z2×Z2-graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. …”
Get full text

Constrained BRST-BFV Lagrangian formulations for higher spin fields in Minkowski spaces by A. A. Reshetnyak

“…The closedness of the superalgebra {Q C , Ô a , σ C i } guarantees that the final gauge-invariant Lagrangian formulation is compatible with the off-shell algebraic constraints Ô a imposed on the field and gauge parameter vectors of the Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to Ô a , in comparison with the vectors for unconstrained BRST-BFV Lagrangian formulation. …”
Get full text

ODE/IM correspondence and supersymmetric affine Toda field equations by Katsushi Ito, Mingshuo Zhu

“…We study the linear differential system associated with the supersymmetric affine Toda field equations for affine Lie superalgebras, which has a purely odd simple root system. …”
Get full text

Fun with F24 by Sarah M. Harrison, Natalie M. Paquette, Daniel Persson, Roberto Volpato

“…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. …”
Get full text

The Diamond Lemma and the PBW Property in Quantum Algebras by M. Havlíček, S. Pošta

“…The approach presented here is successful in other cases of quantum algebras and superalgebras.…”
Get full text