Descent Relations in Cubic Superstring Field Theory

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 and 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.Comment: Replaced to JHEP styl

String Field Theory Projectors for Fermions of Integral Weight

The interaction vertex for a fermionic first order system of weights (1,0) such as the twisted bc-system, the fermionic part of N=2 string field theory and the auxiliary \eta\xi system of N=1 strings is formulated in the Moyal basis. In this basis, the Neumann matrices are diagonal; as usual, the eigenvectors are labeled by \kappa\in\R. Oscillators constructed from these eigenvectors make up two Clifford algebras for each nonzero value of \kappa. Using a generalization of the Moyal-Weyl map to the fermionic case, we classify all projectors of the star-algebra which factorize into projectors for each \kappa-subspace. At least for the case of squeezed states we recover the full set of bosonic projectors with this property. Among the subclass of ghost number-homogeneous squeezed state projectors, we find a single class of BPZ-real states parametrized by one (nearly) arbitrary function of \kappa. This class is shown to contain the generalized butterfly states. Furthermore, we elaborate on sufficient and necessary conditions which have to be fulfilled by our projectors in order to constitute surface states. As a byproduct we find that the full star product of N=2 string field theory translates into a canonically normalized continuous tensor product of Moyal-Weyl products up to an overall normalization. The divergent factors arising from the translation to the continuous basis cancel between bosons and fermions in any even dimension.Comment: LaTeX, 1+23 pages, minor improvements, references adde

UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)

We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a presence of non-integrable IR singularities in noncommutative scalar electrodynamics for general coupling constants. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N=2 SUSY gauge theory.Comment: 9 pages, 16 EPS figure

Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle

A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On-shell it is consistent with lightcone quantization, while off-shell it gives a noncommutative superspace that realizes non-linearly a hidden 11-dimensional super Poincare symmetry. The non-linear commutation rules are then used to construct the supersymmetric generalization of the covariant Moyal star product in noncommutative superspace. As one of the possible applications, we propose this new product as the star product in supersymmetric string field theory. Furthermore, the formalism introduces new techniques and concepts in noncommutative (super)geometry.Comment: 17 pages, LaTe

Schnabl's L_0 Operator in the Continuous Basis

Following Schnabl's analytic solution to string field theory, we calculate the operators ${\cal L}_0,{\cal L}_0^\dagger$ for a scalar field in the continuous $\kappa$ basis. We find an explicit and simple expression for them that further simplifies for their sum, which is block diagonal in this basis. We generalize this result for the bosonized ghost sector, verify their commutation relation and relate our expressions to wedge state representations.Comment: 1+16 pages. JHEP style. Typos correcte

Normalization anomalies in level truncation calculations

We test oscillator level truncation regularization in string field theory by calculating descent relations among vertices, or equivalently, the overlap of wedge states. We repeat the calculation using bosonic, as well as fermionic ghosts, where in the bosonic case we do the calculation both in the discrete and in the continuous basis. We also calculate analogous expressions in field level truncation. Each calculation gives a different result. We point out to the source of these differences and in the bosonic ghost case we pinpoint the origin of the difference between the discrete and continuous basis calculations. The conclusion is that level truncation regularization cannot be trusted in calculations involving normalization of singular states, such as wedge states, rank-one squeezed state projectors and string vertices.Comment: 1+20 pages, 6 figures. v2: Ref. added, typos correcte

Witten's Vertex Made Simple

The infinite matrices in Witten's vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.Comment: 24 pages, 2 figures, RevTeX style, typos correcte

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.Comment: 19 pages, LaTeX, 3 figures. Eqs. (3.2), (3.3) and (4.6) are corrected, and new gauge fixing condition is use

Generalized Kahler geometry and gerbes

We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler potential is discussed.Comment: 28 page