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Register a new userDescent Relations in Cubic Superstring Field Theory
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The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations <V_2|V_1> and <V_3|V_1> in the NS fermionic string field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
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The gauge-fixing problem of modified cubic open superstring field theory is discussed in detail both for the Ramond and Neveu-Schwarz sectors in the Batalin-Vilkovisky (BV) framework. We prove for the first time that the same form of action as the classical gauge-invariant one with the ghost-number constraint on the string field relaxed gives the master action satisfying the BV master equation. This is achieved by identifying independent component fields based on the analysis of the kernel structure of the inverse picture changing operator. The explicit gauge-fixing conditions for the component fields are discussed. In a kind of $b_0=0$ gauge, we explicitly obtain the NS propagator which has poles at the zeros of the Virasoro operator $L_0$.
Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms extend the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like, and we explicitly compute it for super Riemann surfaces.
We reconstruct a complete type II superstring field theory with L-infinity structure in a symmetric way concerning the left- and right-moving sectors. Based on the new construction, we show again that the tree-level S-matrix agrees with that obtained using the first-quantization method. Not only is this a simple and elegant reconstruction, but it also enables the action to be mapped to that in the WZW-like superstring field theory, which has not yet been constructed and fills the only gap in the WZW-like formulation.
We study target space theory on a torus for the states with $N_L+N_R=2$ through Double Field Theory. The spin-two Fierz-Pauli fields are not allowed when all spatial dimensions are non-compact. The massive states provide both non-vanishing momentum and winding numbers in the target space theory. To derive the cubic action, we provide the unique constraint for $N_L eq N_R$ compatible with the integration by part. We first make a correspondence of massive and massless fields. The quadratic action is gauge invariant by introducing the mass term. We then proceed to the cubic order. The cubic action is also gauge invariant by introducing the coupling between the one-form field and other fields. The massive states do not follow the consistent truncation. One should expect the self-consistent theory by summing over infinite modes. Hence the naive expectation is wrong up to the cubic order. In the end, we show that the momentum and winding modes cannot both appear for only one compact doubled space.
In this note, we first explain the equivalence between the interaction Hamiltonian of Green-Schwarz light-cone gauge superstring field theory and the twist field formalism known from matrix string theory. We analyze the role of the large N limit in matrix string theory, in particular in relation with conformal perturbation theory around the orbifold SCFT that reproduces light-cone string perturbation theory. We show how the scaling with N is directly related to measures on the moduli space of Riemann surfaces. The scaling dimension 3 of the Mandelstam vertex as reproduced by the twist field interaction is in this way related to the dimension 3(h-1) of the moduli space. We analyze the structure and scaling of the higher order twist fields that represent the contact terms. We find one relevant twist field at each order. More generally, the structure of string field theory seems more transparent in the twist field formalism. Finally we also investigate the modifications necessary to describe the pp-wave backgrounds in the light-cone gauge and we interpret a diagram from the BMN limit as a stringy diagram involving the contact term.
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