Ramond Sector Research Articles

NSR singular vectors from Uglov polynomials

It was conjectured by Belavin et al. [J. High Energy Phys. 2013(3), 35] that bosonization of a singular vector (in the Neveu–Schwarz sector) of the N=1 super analog of the Virasoro algebra can be identified with the Uglov symmetric function. In this paper, we prove this conjecture. We also extend this result to the Ramond sector of the N=1 super-Virasoro algebra.

Super topological recursion and Gaiotto vectors for superconformal blocks

We investigate a relation between the super topological recursion and Gaiotto vectors for $\mathcal{N}=1$ superconformal blocks. Concretely, we introduce the notion of the untwisted and $\mu$-twisted super topological recursion, and construct a dual algebraic description in terms of super Airy structures. We then show that the partition function of an appropriate super Airy structure coincides with the Gaiotto vector for $\mathcal{N}=1$ superconformal blocks in the Neveu-Schwarz or Ramond sector. Equivalently, the Gaiotto vector can be computed by the untwisted or $\mu$-twisted super topological recursion. This implies that the framework of the super topological recursion -- equivalently super Airy structures -- can be applied to compute the Nekrasov partition function of $\mathcal{N}=2$ pure $U(2)$ supersymmetric gauge theory on $\mathbb{C}^2/\mathbb{Z}_2$ via a conjectural extension of the Alday-Gaiotto-Tachikawa correspondence.

Mathcal{N} = 4 SYM, Argyres-Douglas theories, and an exact graded vector space isomorphism

In this first of two papers, we explain in detail the simplest example of a broader set of relations between apparently very different theories. Our example relates mathfrak{su}(2) mathcal{N} = 4 super Yang-Mills (SYM) to a theory we call “(3, 2)”. This latter theory is an exactly marginal diagonal SU(2) gauging of three D3(SU(2)) Argyres-Douglas (AD) theories. We begin by observing that the Schur indices of these two theories are related by an algebraic transformation that is surprisingly reminiscent of index transformations describing spontaneous symmetry breaking on the Higgs branch. However, this transformation breaks half the supersymmetry of the SYM theory as well as its full mathcal{N} = 2 SU(2)F flavor symmetry. Moreover, it does so in an interesting way when viewed through the lens of the corresponding 2D vertex operator algebras (VOAs): affine currents of the small mathcal{N} = 4 super-Virasoro algebra at c = −9 get mapped to the mathcal{A}(6) stress tensor and some of its conformal descendants, while the extra supersymmetry currents on the mathcal{N} = 4 side get mapped to higher-dimensional fermionic currents and their descendants on the mathcal{A}(6) side. We prove these relations are facets of an exact graded vector space isomorphism (GVSI) between these two VOAs. This GVSI respects the U(1)r charge of the parent 4D theories. We briefly sketch how more general mathfrak{su}(N) mathcal{N} = 4 SYM theories are related to an infinite class of AD theories via generalizations of our example. We conclude by showing that, in this class of theories, the mathcal{A}(6) VOA saturates a new inequality on the number of strong generators.

Classification of simple Harish-Chandra modules over the Neveu-Schwarz algebra and its contact subalgebra

In this paper, we classify all simple jet modules for the Neveu-Schwarz algebra k ˆ and its contact subalgebra k + . Based on these results, we give a classification of simple Harish-Chandra modules for k ˆ and k + .

Bootstrapping fermionic rational CFTs with three characters

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γθ, Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound hR ≥ frac{C}{24} , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group.

Characters and quantum reduction for orthosymplectic Lie superalgebras

In this study, we study principal admissible representations for the affine Lie superalgebra [Formula: see text]. Using the character formula of irreducible admissible representations of [Formula: see text], we calculate a character formula of [Formula: see text]-modules which are obtained from the quantized Drinfeld–Sokolov reduction and principal admissible representations. As a by-product, we obtain the minimal series modules of the Neveu–Schwarz algebra through the [Formula: see text]-modules arising from the principal admissible modules over [Formula: see text].

Cosmology at the top of the \u03b1\u2032 tower

The cosmology of the fully α′-corrected duality-invariant action for the Neveu-Schwarz sector of string theory is revisited, with special emphasis on its coupling to matter sources. The role of the duality covariant pressure and dilatonic charge of the matter sector is explored in various contexts, from the low-curvature regime to non-perturbative solutions in α′. We comment on how an infinite tower of α′ corrections allows for fixed-dilaton de Sitter solutions, even in vacuum. We further investigate the necessary conditions for accelerated expansion in the Einstein frame, as well as for non-singular bounces that could resolve the big bang singularity. In particular, explicit examples are constructed, which show that the tower of α′ corrections may support an Einstein-frame non-singular cosmological bouncing background, even when the matter sector respects the null energy condition.

2-Local superderivations on the super Virasoro algebra and the super W(2,2) algebra

The present paper is devoted to studying 2-local superderivations on the super Virasoro algebra and the super algebra. It is proved that all 2-local superderivations on the super Virasoro algebra as well as the super algebra are (global) superderivations.

Direct limit completions of vertex tensor categories

We show that direct limit completions of vertex tensor categories inherit vertex and braided tensor category structures, under conditions that hold for example for all known Virasoro and affine Lie algebra tensor categories. A consequence is that the theory of vertex operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid and non-degenerate vertex tensor categories of certain modules for both the affine vertex superalgebra of [Formula: see text] and the [Formula: see text] super Virasoro algebra to categories of Virasoro algebra modules via certain cosets.

Punctures and p-Spin Curves from Matrix Models II

We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for p=1/2 and p=3/2. In those new cases one finds contributions from the Ramond sector, which were not present for positive integer p.The existence of Virasoro constraints, in particular a string equation, is considered also for half-integral spins. The contribution of the boundary of a Riemann surface, is investigated through a logarithmic matrix model The supersymmetric random matrices provide extensions to mixed positive and negative p punctures.

Renormalization of twisted Ramond fields in D1-D5 SCFT2

We explore the n-twisted Ramond sector of the deformed two-dimensional mathcal{N} = (4, 4) superconformal (T4)N/SN orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-N limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-N limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.

Super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras

We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner.

Lessons from the Ramond sector

We revisit the consistency of torus partition functions in (1+1)d fermionic conformal field theories, combining old ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization dualities. Various lessons can be learned by simply examining the oft-ignored Ramond sector. For several extremal/kinky modular functions in the bootstrap literature, we can either rule out or identify the underlying theory. We also revisit the N = 1 Maloney-Witten partition function by calculating the spectrum in the Ramond sector, and further extending it to include the modular sum of seed Ramond characters. Finally, we perform the full N = 1 RNS modular bootstrap and obtain new universal results on the existence of relevant deformations preserving different amounts of supersymmetry.

Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector

We analyze the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector. We show that their partition functions can be expressed as the infinite sums of the homogeneous operators acting on the elementary functions. In spite of the fact that the usual W-representations of these matrix models can not be provided here, we can still derive the compact expressions of the correlators in these two supereigenvalue models. Furthermore, the non-Gaussian (chiral) cases are also discussed.

Classification of simple Harish-Chandra modules over the N = 1 Ramond algebra

In this paper, we give a new approach to classify all Harish-Chandra modules for the N=1 Ramond algebra s based on the so called A-cover theory developed in [1].

On non-weight representations of the N = 2 superconformal algebras

In this paper, we construct a family of non-weight modules over the untwisted $N=2$ superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank $2$. We give a classification of isomorphism classes of such modules. Moreover, all submodules of such modules are precisely determined. In particular, those modules are not simple. The corresponding simple quotient modules are classified. Furthermore, these simple modules when restricted as modules over $N=1$ superconformal algebras coincide with those modules constructed in [H. Yang, Y. Yao, L. Xia, A family of non-weight modules over the super-Virasoro algebras, J. Algebra 547 (2020), 538-555].

Correlators in the supereigenvalue model in the Ramond sector

We investigate the supereigenvalue model in the Ramond sector. We prove that its partition function can be obtained by acting on elementary functions with exponents of the given operators. The Virasoro constraints for this supereigenvalue model are presented. The remarkable property of these bosonic constraint operators is that they obey the Witt algebra and null 3-algebra. The compact expression of correlators can be derived from these Virasoro constraints.

The shadow of dark matter as a shadow of string theory: string origin of the dipole term

We point out that the Kalb–Ramond field can couple to the Ramond and Neveu–Schwarz fields of superstring theory in a way that can generate a coupling of the Kalb–Ramond field to dark matter dipole moments. Electroweak dipole dark matter could then arise from the Ramond sector of superstrings with low string scale M_slesssim 120 TeV.

String coherent vertex operators of Neveu-Schwarz and Ramond states

We present a compact expression for a coherent vertex operator in superstring theory, in the Neveu-Schwarz sector, that can be easily extended to the Ramond sector by supersymmetric transformations in target space. We give also an explicit construction for the Ramond coherent vertex operator. These constructions provide the use of the supersymmetric version of the Del Giudice-Di Vecchia-Fubini operators and Operator Product Expansion techniques, displaying manifest BRST invariance and after normal ordering also manifest covariance. As a consistency check we compute tree level three-point scattering amplitudes involving Neveu-Schwarz coherent vertex operators in different superghost pictures. Extending these results to the closed superstring, we give the expressions of the coherent vertex operators in the case of type IIA and IIB theories.

ADMISSIBLE LEVEL mathfrak{osp}left(1left|2right.right) MINIMAL MODELS AND THEIR RELAXED HIGHEST WEIGHT MODULES

The minimal model mathfrak{osp}left(1|2right) vertex operator superalgebras are the simple quotients of affine vertex operator superalgebras constructed from the affine Lie super algebra hat{mathfrak{osp}}left(1left|2right.right) at certain rational values of the level k. We classify all isomorphism classes of ℤ2-graded simple relaxed highest weight modules over the minimal model mathfrak{osp}left(1|2right) vertex operator superalgebras in both the Neveu–Schwarz and Ramond sectors. To this end, we combine free field realisations, screening operators and the theory of symmetric functions in the Jack basis to compute explicit presentations for the Zhu algebras in both the Neveu–Schwarz and Ramond sectors. Two different free field realisations are used depending on the level. For k < −1, the free field realisation resembles the Wakimoto free field realisation of affine mathfrak{sl}(2) and is originally due to Bershadsky and Ooguri. It involves 1 free boson (or rank 1 Heisenberg vertex algebra), one βγ bosonic ghost system and one bc fermionic ghost system. For k > −1, the argument presented here requires the bosonisation of the βγ system by embedding it into an indefinite rank 2 lattice vertex algebra.