Recently an action for open superstring field theory was proposed where the Neveu-Schwarz sector is formulated in the large Hilbert space while the Ramond sector lives in a restriction of the small Hilbert space. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
We consider the algebraic effective couplings for open superstring massless modes in the framework of the $A_\infty$ theory in the small Hilbert space. Focusing on quartic algebraic couplings, we reduce the effective action of the $A_\infty$ theory to the Berkovits one where we have already shown that such couplings are fully computed from contributions at the boundary of moduli space, when the massless fields under consideration are appropriately charged under an ${\cal N}\!=\!2$ $R$-symmetry. Here we offer a proof of localization which is in the small Hilbert space. We also discuss the flat …
This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed eff…
We construct a complete type II superstring field theory that includes all the NS-NS, R-NS, NS-R and R-R sectors. As in the open and heterotic superstring cases, the R-NS, NS-R and R-R string fields are constrained by using the picture-changing operators. In particular, we use a non-local inverse picture-changing operator for the constraint on the R-R string field, which seems to be inevitable due to the compatibility of the extra constraint with the closed string constraints. The natural symplectic form in the restricted Hilbert space gives a non-local kinetic action for the R-R sector, but i…
We revisit the calculation of the thermal free energy for string theory in three-dimensional anti-de Sitter spacetime with Neveu-Schwarz-Neveu-Schwarz flux. The path integral calculation is exploited to confirm the off-shell Hilbert space and we find that the Casimir of the discrete representations of the isometry group takes values in a half-open interval. We extend the free energy calculation to the case of superstrings, calculate the boundary toroidal twisted partition function in the Ramond-Ramond sector, and prove lower bounds on the boundary conformal dimension from the bulk perspective.…
Hilbert Space of Space-time SCFT in AdS_3 Supersting and T^{4kp}/S_{kp} SCFT
我们在hep-th/9806194给出的框架下研究AdS_3 x S^3 x T^4上的超弦理论。我们讨论了“时空CFT”的希尔伯特空间，特别是从整体超弦理论的物理自由度出发，构造了一个合适的时空CFT真空。我们首先在p=1的情况下明确地构造它，然后提出p>1的一般情况的建议。在完成了GKS的高阶模算符（特别是包含自旋场的高阶模算符）的构造之后，我们还比较了时空CFT和T^{4 kp}/ S_{kp} SCFT，即两种理论中手征原色的物理谱和玻色子和费米子振子的代数结构。我们还观察到我们关于时空CFT的希尔伯特空间的建议如何在p>1的情况下导致两种理论的手征原色谱之间的令人满意的对应。
Superstrings on PP-Wave Backgrounds and Symmetric Orbifolds
本文研究了pp波背景下的超弦理论，其中NSNS通量被实现为AdS_3 × S^3 × M^4的Penrose极限，其中M^4是T^4或T^4/Z_2（~ K3）。在协变规范下量子化该系统，我们明确地构造了时空超对称代数和DDF算符的完备集。我们利用流代数的谱流表示分析物理态的谱。这个谱是按照AdS_3弦论中的"短弦扇区“和"长弦扇区”来分类的。后者的态沿pp波背景的横截面自由传播，而前者的态则不然。我们比较了AdS_3 x S^3 x M^4超弦对偶理论的候选者--对称轨道共形理论中具有大R-荷的BPS态和几乎BPS态与短弦谱。我们证明了每一个短弦态都可以成功地嵌入到对称轨道共形理论的单粒子希尔伯特空间中。
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert action coupled with gauge fields, and formulate superstring theory non-perturbatively by summing over metrics and the gauge fields on the spaces of strings. This theory does not depend on backgrounds. The theory has a supersymmetry as a part of the diffeomorphisms symmetry on the s…
The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension $d$ and the highest order $k$ of the Lanczos-Lovelock densities appearing in the action. Three typical example cases with $(d,k)=(5,1), (5,2)$ and $(6,2)$ are chosen as example cases and studied in some detail. These cases are representatives of Einstein-Hilbert, Chern-Simons and Born-Infield like gravity models. Our study indicat…
We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proof requires a different procedure) and extend to the quaternionic case a result concerning the classification of irreducible von Neumann algebras. Secondly, we consider elementary relativistic systems in Wigner's view defined as a locally-faithful irreducible strongly-continuous unitary representation of Poincaré group in quaternionic Hilbert space. We prove that, if the squared-mass operator is non-negative, the syst…
