On semiclassical equivalence of Green–Schwarz and pure spinor strings in AdS(5) × S(5)

Abstract

We present a method to study the equivalence at the semiclassical level of the Green-Schwarz and pure spinor formulations of String Theory in AdS(5) × S(5). This method provides a clear separation of the physical and unphysical sectors of the pure spinor formulation and allows to prove that the two models have not only equal spectra of the fermionic fluctuations but also equal conformal weights (the bosonic ones being equal by construction).

AdS pure spinor superstring in constant backgrounds

“…The result agreed with the strong coupling computation using the Y-system [14]. Some aspects of semiclassical quantization of the AdS pure spinor superstring have been discussed in [15,16,17].…”

“…Consider the BRST symmetry first. The transformation for the world-sheet fields are given by (17). Note that they start with a term linear in (X, λ, ω, λ, ω), then…”

A minimalistic pure spinor sigma-model in AdS

“…Therefore elements of g2 are vectors from this tangent space. We can also consider the tangent space to the full superspace M: M M = super(AdS 5 × S 5 ) = P SU(2, 2|4) SO(1, 4) × SO (5) (43)…”

“…In this paper we will show, closely following [4,5], that the pure spinor terms (2) can actually be removed by reduction to a smaller BV phase space, keeping intact all the symmetries of AdS 5 × S 5 . The resulting action is degenerate, and therefore can not be immediately used for quantization.…”

Master symmetry in the AdS 5 × S 5 pure spinor string

“…There is hope such a task can be done, since it was shown by explicit computations in references [20,21] that the semi-classical quantization of the pure spinor string is equivalent to the Green-Schwarz string in a certain class of solutions. In [34] it was argued that the equivalence holds for any physical solution. With these results in mind, it is likely that one can extend the results of, for example, references [35,36] to the pure spinor string.…”