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Register a new userMatrix string theory, contact terms, and superstring field theory
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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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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.
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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.
Kaluza-Klein compactifications of higher dimensional Yang-Mills theories contain a number of four dimensional scalars corresponding to the internal components of the gauge field. While at tree-level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1-loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK--modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius $R$ is much bigger than the scale of the UV completion ($R gg sqrt{alpha},a$), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in $mathcal N=2,4$ Super Yang-Mills is highly suppressed due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.
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