String theory in the Penrose limit ofAdS2×S2spacetime

Abstract

The string theory in the Penrose limit of AdS 2 ×S 2 is investigated. The specific Penrose limit is the background known as the Nappi-Witten spacetime, which is a plane-wave background with an axion field. The string theory on it is given as the Wess-Zumino-Novikov-Witten (WZNW) model on non-semi-simple group H 4 . It is found that, in the past literature, an important type of irreducible representations of the corresponding algebra, h 4 , were missed. We present this "new" representations, which have the type of continuous series representations. All the three types of representations of the previous literature can be obtained from the "new" representations by setting the momenta in the theory to special values. Then we realized the affine currents of the WZNW model in terms of four bosonic free fields and constructed the spectrum of the theory by acting the negative frequency modes of free fields on the ground level states in the h 4 continuous series representation. The spectrum is shown to be free of ghosts, after the Virasoro constraints are satisfied. In particular we argued that there is no need for constraining one of the longitudinal momenta to have unitarity. The tachyon vertex operator, that correspond to a particular state in the ground level of the string spectrum, is constructed. The operator products of the vertex operator with the currents and the energy-momentum tensor are shown to have the correct forms, with the correct conformal weight of the vertex operator.

Isometric embeddings and noncommutative branes in homogeneous gravitational waves

“…However, as we discuss in detail in this paper, the Penrose-Güven limit of AdS 2 × S 2 does not induce the full NS-supported geometry of the NW 4 spacetime. Therefore, contrary to some claims [26,74], the four-dimensional Nappi-Witten spacetime cannot be studied as the Penrose-Güven limit of AdS 2 × S 2 . Instead, it arises as a Penrose-Güven limit of the near horizon geometry of NS5-branes [33], on which string theory is dual to little string theory.…”

“…26) on the null hypersurfaces of constant x − = x − 0 , and computing the corresponding two-form gauge transformation of the B-field in (2.27) to getB Λ 6 := B 6 + dΛ = − i µ dx + ∧ z ⊤ dz − z ⊤ dz + 2 i µ −1 x − 0 dz ⊤ ∧ dz . (6.27) …”