Nathan Berkovits

Super-Poincaré covariant quantization of the superstring

Inst. de Fis. Teorica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo, SP

N = 4 topological strings

Abstract We show how to make a topological string theory starting from an N = 4 superconformal theory. The critical dimension for this theory is c = 2 (c = 6) . It is shown that superstrings (in both the RNS and GS formulations) and critical N = 2 strings are special cases of this topological theory. Applications for this new topological theory include: (1) Proving the vanishing to all orders of all scattering amplitudes for the self-dual N = 2 string with flat background, with the exception of the three-point function and the closed-string partition function; (2) Showing that the topological partition function of the N = 2 string on the K 3 background may be interpreted as computing the superpotential in harmonic superspace generated upon compactification of type II superstrings from 10 to 6 dimensions; and (3) Providing a new prescription for calculating s uperstring amplitudes which appears to be free of total-derivative ambiguities.

Superstring theory on AdS2 × S2 as a coset supermanifold

Instituto de Fisica Teorica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo

Super-Poincaré invariant superstring field theory

Abstract Using the topological techniques developed in an earlier paper with Vafa, a field theory action is constructed for any open string with critical N = 2 worldsheet superconformal invariance. Instead of the Chem-Simons-like action found by Witten, this action resembles that of a Wess-Zumino-Witten model. For the N = 2 string which describes (2,2) self-dual Yang-Mills, the string field generalizes the scalar field of Yang. As was shown in recent papers, an N = 2 string can also be used to describe the Green-Schwarz superstring in a Calabi-Yau background. In this case, one needs three types of string fields which generalize the real superfield of the super-Yang-Mills prepotential, and the chiral and anti-chiral superfields of the Calabi-Yau scalar multiplet. The resulting field theory action for the open superstring in a Calabi-Yau background has the advantages over the standard RNS action that it is manifestly SO(3,1) super-Poincare invariant and does not require contact terms to remove tree-level divergences.

Tachyon condensation in superstring field theory

Abstract It has been conjectured that at the stationary point of the tachyon potential for the D-brane–anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess–Zumino–Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by condensation of the tachyon field alone. While the action is non-polynomial, the multiscalar tachyon potential to any fixed level involves only a finite number of interactions. We compute this potential to level three, obtaining 85% of the expected vacuum energy, a result consistent with convergence that can also be viewed as a successful test of the string field theory. The resulting effective tachyon potential is bounded below and has two degenerate global minima. We calculate the energy density of the kink solution interpolating between these minima finding good agreement with the tension of the D-brane of one lower dimension.

Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable

Conformal supergravity in twistor-string theory

b

Alternative string theory in twistor space for N=4 super-Yang-Mills theory

ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that

Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring

R^4

Superstrings in graviphoton background and N=1/2+3/2 supersymmetry

terms in the effective action receive no perturbative contributions above one loop.