Leszek Hadasz, Zbigniew Jaskolski, Paulina Suchanek
The structure of the 4-point N=1 super-conformal blocks in the Ramond sector is analyzed. The elliptic recursion relations for these blocks are derived.
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N=2 Superconformal Description of Superstring in Ramond-Ramond Plane Wave Backgrounds
利用10年前发展起来的U（4）形式，给出了Ramond-Ramond平面波背景中超弦的世界片作用量的N=（2，2）超共形不变性.这简化了一致的Ramond-Ramond平面波背景的构造，并消除了与光锥相互作用点算子相关的问题。
Null vectors of the superconformal algebra: the Ramond sector
我们考虑了$N=1$超共形代数的Ramond扇区，并利用Bauer等人的融合原理找到了奇异向量在可约最高权Verma模表示中的表达式.
We use AGT correspondence between N=2 SUSY Yang-Mills theory on ${\mathbb R}^4/{\mathbb Z}_2$ and two-dimensional CFT model with the algebra $ {\cal H} \oplus \hat{sl}(2)_2 \oplus \text{NSR}$ to obtain the explicit expressions for 4-point NSR conformal blocks including Ramond fields in terms of Nekrasov partition functions and correlation functions of $\hat{sl}(2)_2$ WZW model.
The Virasoro logarithmic minimal models were intensively studied by several groups over the last ten years with much attention paid to the fusion rules and the structures of the indecomposable representations that fusion generates. The analogous study of the fusion rules of the $N=1$ superconformal logarithmic minimal models was initiated in arXiv:1504.03155 as a continuum counterpart to the lattice explorations of arXiv:1312.6763. These works restricted fusion considerations to Neveu-Schwarz representations. Here, this is extended to include the Ramond sector. Technical advances that make thi…
String theory on AdS3 space-times with boundary conditions that allow for black hole states has global asymptotic symmetries which include an infinite dimensional conformal algebra. Using the conformal current algebra for sigma-models on PSU(1,1|2), we explicitly construct the R-symmetry and Virasoro charges in the worldsheet theory describing string theory on AdS3 X S3 with Ramond-Ramond fluxes. We also indicate how to construct the full boundary superconformal algebra. The boundary superconformal algebra plays an important role in classifying the full spectrum of string theory on AdS3 with R…
The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
本文描述了N=1超对称对数共形场论的Neveu-Schwarz和Ramond扇区的一般特征。我们详细地研究了三个特殊的系统--D-膜反冲，c=-2模型的超共形扩展和超对称SU（2）_2WZW模型。
General 1-point toric blocks in all sectors of N=1 superconformal field theories are analyzed. The recurrence relations for blocks coefficients are derived by calculating their residues and large $Δ$ asymptotics.
Ramond sector of superconformal algebras via quantum reduction
在扭曲情形下研究仿射超代数的量子哈密尔顿约化。对“极小”超共形W-代数的Ramond扇区进行了详细的刻画，得到了其行列式公式。广泛的例子列表包括所有秩为2的单李超代数。本文将Kac和Wakimoto（math-ph/0304011）的结果推广到扭转情况。
Construction Formulae for Singular Vectors of the Topological and of the Ramond N=2 Superconformal Algebras
给出了Neveu-Schwarz N=2超共形代数的奇异向量与拓扑和Ramond N=2超共形代数的$16 + 16$型奇异向量之间的一一映射.其结果是，一个获得的构造公式，后者使用的构造公式的Neveu-Schwarz奇异向量由于Dörrzapf。拓扑和Ramond N=2代数的不可分解奇异向量（“无标号”和“无螺旋性”奇异向量）不能映射到Neveu-Schwarz N=2代数的奇异向量上，而映射到{ \it subsingular}向量上，因为不存在构造公式。
We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models SM_p for p>> 1. We explain how to compute the NS and Ramond fields conformal blocks in the leading order in 1/p and follow the renormalization scheme propsed in [1]. As a result we obtained the anomalous dimensions of certain NS and Ramond fields. It turns out that the linear combination expressing the infrared limit of these fields in term of the IR theory SM_{p-2} is exactly the same as those of the nonsupersymmetric minimal theory.
Dynamical Description of Spectral Flow in N=2 Superconformal Field Theories
我们展示了如何在N=2超共形场论的Neveu-Schwarz和Ramond扇区之间的谱流可以在三维空间中描述的带电粒子的传播耦合到一个陈-西蒙斯规范理论。简并的陈-西蒙斯真空之间的量子力学混合在两个扇区的不同边界条件之间插值，因此为GSO投影提供了动力学图像。
Interpretation of the Determinant Formulae for the Chiral Representations of the N=2 Superconformal Algebra
我们证明了非周期NS代数和周期R代数的N=2行列式公式可以直接应用于分别建立在手征初态和Ramond基态上的不完全Verma模，只要以适当的方式修改零点的解释。也就是说，行列式公式的零点说明了建立在手征原色和Ramond基态上的最高权奇异态，但是奇异态的能级和相对U（1）电荷的识别与完全Verma模不同。特别地，二次消失面$f^A_{r,s}=0$和$f^P_{r,s}=0$的零点的一半对应于不带电的奇异态，而另一半对应于带电的奇异态。我们推导了建立在手征基元上的奇异态谱，包括扭曲拓扑代数的奇异态和建立在Ramond基态上的奇异态谱。我们还发现了非最高权奇异态的存在性，这些奇异态不是任何最高权奇异态的次态。
Fusion Rules in N=1 Superconformal Minimal Models
推广到N=1超共形极小模型的模块化变换矩阵和融合规则之间的关系，在合理的共形场论，Verlinde定理，示出提供完整的信息融合规则，包括其费米子宇称。超共形三临界Ising和Ashkin-Teller模型的结果与已知的有理共形公式一致。本文还讨论了N=1个极小模型的Ramond扇区中关联函数的库仑气体描述，并完成了以前的公式。
In this paper we consider unitary highest weight irreducible representations of the `Large' $\mathcal{N}=4$ superconformal algebra $A_γ$ in the Ramond sector as infinite-dimensional graded modules of its zero mode subalgebra, $\mathfrak{su}(2|2)$. We describe how representations of $\mathfrak{su}(2|2)$ may be classified using Young supertableaux, and use the decomposition of $A_γ$ as an $\mathfrak{su}(2|2)$ module to discuss the states which contribute to the supersymmetric index $I_1$, previously proposed in the literature by Gukov, Martinec, Moore and Strominger.
Key to the exact solubility of the unitary minimal models in two-dimensional conformal field theory is the organization of their Hilbert space into Verma modules, whereby all eigenstates of the Hamiltonian are obtained by the repeated action of Virasoro lowering operators onto a finite set of highest-weight states. The usual representation-theoretic approach to removing from all modules zero-norm descendant states generated in such a way is based on the assumption that those states form a nested sequence of Verma submodules built upon singular vectors, i.e., descendant highest-weight states. W…
The explicit formula for the superconformal singular vectors in the Neveu-Schwarz sector has been obtained recently, via its symmetric polynomial representation, as a sum of Jack superpolynomials. Here we present the analogous, but slightly more complicated, closed-form expression for the Ramond singular vectors.
As a step toward deeper understanding of the AdS/CFT correspondence, exact quantization of a Brink-Schwarz superparticle in the AdS_5 x S^5 background with Ramond-Ramond (RR) flux is performed from the first principle in the phase space formulation. It includes the construction of the quantum Noether charges for the psu(2,2|4) superconformal symmetry and by solving the superconformal primary conditions we obtain the complete physical spectrum of the system with the explicit wave functions. The spectrum agrees precisely with the supergravity results, including all the Kaluza-Klein excitations. …
Elliptic recurrence representation of the N=1 Neveu-Schwarz blocks
我们应用Al. Zamolodchikov的适当推广的方法，导出Neveu-Schwarz超共形块的椭圆递归表示
Light-cone gauge superstring theory in noncritical dimensions corresponds to a worldsheet theory with nonstandard longitudinal part in the conformal gauge. The longitudinal part of the worldsheet theory is a superconformal field theory called X^{\pm} CFT. We show that the X^{\pm} CFT combined with the super-reparametrization ghost system can be described by free variables. It is possible to express the correlation functions in terms of these free variables. Bosonizing the free variables, we construct the spin fields and BRST invariant vertex operators for the Ramond sector in the conformal gau…
Ramond Sector Characters and N=2 Landau-Ginzburg Models
本文给出了E.威腾我们的建设使我们能够推广这些表达式的D和E系列的N=2的极小模型，以及其他N=2 Kazama-铃木陪集模型，如$SU(N)\times SO(2(N-1))/SU(N-1)\times U(1)$。我们验证了这些表达式确实符合相应的Landau-Ginzburg“椭圆亏格”，一定的拓扑不变扭曲路径积分的有效Landau-Ginzburg作用，我们得到使用Witten的方法。我们表明我们的方法可以用来构建（或排除）可能的朗道-金斯堡潜力描述其他N=2超共形理论。
All types of 4-point spheric conformal blocks in both sectors of N=1 superconformal field theory are introduced and analyzed. The elliptic recurrence formulae are derived for all the types of blocks not previously discussed in the literature. The results are used for numerical verification of the crossing symmetry of some 4-point functions in the N=1 superconformal Liouville field theory.
We examine the behavior of the Ramond ground states in the D1-D5 CFT after a deformation of the free-orbifold sigma model on target space $({\mathbb T}^4)^N / S_N$ by a marginal interaction operator. These states are compositions of Ramond ground states of the twisted and untwisted sectors. They are characterized by a conjugacy class of $S_N$ and by the set of their "spins", including both R-charge and "internal" SU(2) charge. We compute the four-point functions of an arbitrary Ramond ground state with its conjugate and two interaction operators, for genus-zero covering surfaces representing t…
We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the colliding limit of supersymmetric vertex operators of NS sector and half-odd integer to the Ramond sectors. The spectral curve is simply integrable at Nekrasov-Shatashvili limit and the partition function (inner product of irregular conformal state) is obtained from the superconformal structure manifest in the spectral curve. We present some explicit forms of th…
Recursion representation of the Neveu-Schwarz superconformal block
用偶超投射不变量的幂级数定义了N = 1 Neveu-Schwarz代数的四点超共形块.这些展开式的系数既表示为“中间”共形权中的极点之和，也表示为代数的中心荷中的极点之和。在这两种情况下，计算这些极点的残差。封闭的递推关系的块系数推导。
We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is inv…
On Stochastic Evolutions and Superconformal Field Theory
在SLE领域中，通过利用维拉索罗代数的最高权模中的奇异向量，研究了共形映射的某些随机演化与共形场论之间的联系。最近发现，这种情况可以扩展到随机演化的超共形映射的N=1超空间的超共形场论和奇异向量的N=1超共形代数的Neveu-Schwarz部门。在这里我们讨论类似的扩展到雷蒙部门。我们还讨论了如何修改的链接时，一个非常规的超共形结构或超导数。
We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ 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 f…
It is now well known that non-local observables in critical statistical lattice models, polymers and percolation for example, may be modelled in the continuum scaling limit by logarithmic conformal field theories. Fusion rules for such theories, sometimes referred to as logarithmic minimal models, have been intensively studied over the last ten years in order to explore the representation-theoretic structures relevant to non-local observables. Motivated by recent lattice conjectures, this work studies the fusion rules of the $N=1$ supersymmetric analogues of these logarithmic minimal models in…
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 $μ$-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 $μ$-twisted super topological r…
We derive the corrections to the conformal dimensions of twisted Ramond ground states in the deformed two-dimensional $\mathcal N = (4,4)$ superconformal $(\mathbb T^4)^N/S_N$ orbifold theory describing bound states of the D1-D5 brane system in type IIB superstring theory. Our result holds to second order in the deformation parameter, and at the large $N$ planar limit. The method of calculation involves the analytic evaluation of integrals of four-point functions of two R-charged twisted Ramond fields and two marginal deformation operators. We also calculate the deviation from zero, at first o…
We describe the effect of the marginal deformation of the $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-$N$ approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scali…
Factorization and Discrete States in C=1 Superliouville Theory
研究了二维超引力作用下$\hat c=1$超共形物质的离散态结构。利用散射振幅的因式分解性质来识别这些状态并构造相应的顶点算子。对于Neveu-Schwarz和Ramond扇区，这些状态被证明是在SU（2）多重态中组织的。在宇宙学常数为零的极限下计算了离散态生成的代数。
Structure Constants in the $N=1$ Super-Liouville Field Theory
二维$N=1$ Super-Liouville场论的对称代数是无限维$N=1$超共形代数，它允许人们证明包含退化场的关联函数服从某些偏线性微分方程.在四点函数的特殊情况下，包括在第一级退化的一次场，该微分方程可以通过超几何函数求解。考虑到场的互定域性，并通过研究s道和t道奇异性，我们得到了三点关联函数的一些函数关系。解此函数方程，我们得到三点函数在Neveu-Schwarz和Ramond部门。
The Adapted Ordering Method in Representation Theory
1998年，自适应排序方法被发展用于超共形代数的表示理论。这种方法，这被证明是非常强大的，可以适用于大多数代数和超代数，但是。它允许：确定给定类型的奇异向量空间的最大维数，仅通过几个系数识别所有奇异向量，发现子奇异向量，并为构造嵌入图设置基础。本文给出了一般代数和超代数的自适应排序方法，并简要地回顾了维拉索罗代数和N=2及Ramond N=1超共形代数的结果。
Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
本文利用广义对称性，在 Calabi-Yau sigma 模型中提出了 Hodge 轨迹的类比，通过非平凡有理 Hodge 自同态的出现来刻画，并分析了椭圆曲线和 K3 曲面的情况。
Ramond from Random: Weil-Petersson Volumes for Super-Riemann surfaces with NS Boundaries and R Punctures
本文通过随机矩阵模型统一处理NS边界和R尖点，计算了超黎曼曲面模空间的Weil-Petersson体积，并首次给出了包含R尖点的谱曲线，利用拓扑递归推导了闭式公式。
A quantum deformation of the ${\mathcal N}=2$ superconformal algebra
本文引入带复参数q、k的幺正结合代数𝒮𝒱𝒾𝓇_q,k作为𝒩=2超共形代数的量子形变，通过计算低阶Kac行列式提出因式分解猜想并获筛选算子支持，证明q→1时可恢复原代数，还给出基于量子仿射代数Wakimoto表示扭转的非平凡海森堡表示。
Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal $\mathfrak{gl}_2$
本文构造 $\mathfrak{gl}_2$ 型量子环面代数的表示，得到生成元 $W_i(z)$，其代数结构为自由费米子代数与 $N=1$ 超 Virasoro 代数的直和的 $q$-形变，并证明其 screening 流与退化极限及二次关系。
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