Chiral strings, the sectorized description and their integrated vertex operators

Abstract

A chiral string can be seen as an ordinary string in a singular gauge for the worldsheet metric and has the ambitwistor string as its tensionless limit. As proposed by Siegel, there is a one-parameter (β) gauge family interpolating between the chiral limit and the usual conformal gauge in string theory. This idea was used to compute scattering amplitudes of tensile chiral strings, which are given by standard string amplitudes with modified (βdependent) antiholomorphic propagators.Due to the absence of a sensible definition of the integrated vertex operator, there is still no ordinary prescription for higher than 3-point amplitude computations directly from the chiral model. The exception is the tensionless limit.In this work this gap will be filled. Starting with a chiral string action, the integrated vertex operator is defined, relying on the so-called sectorized interpretation. As it turns out, this construction effectively emulates a left/right factorization of the scattering amplitude and introduces a relative sign flip in the propagator for the sector-split target space coordinates. N -point tree-level amplitudes can be easily shown to coincide with the results of Siegel et al. * renannlj@fzu.cz

Green-Schwarz and pure spinor formulations of chiral strings

“…Furthermore, the standard Faddeev-Popov method applied to the pure spinor chiral string introduces b-ghost and delta-function insertions in the path integral which allow us to define integrated vertex operators. Remarkably, the delta-function operator is shown to coincide with the sector-splitting operator recently proposed in [24] from the requirement of BRST-closedness of integrated vertex operators. We finally use the so-called physical operators of 10D super-Yang-Mills [25] to obtain explicit expressions for such vertices.…”

“…To compute scattering amplitudes one needs to introduce integrated vertex operators. These operators have recently been constructed in [24] from the action of the so-called sector-splitting operator on unintegrated vertices. The origin of this operator can naturally be understood in the chiral string framework from the following comparison with the standard description of superstrings.…”

“…The integrand of eq. (5.26) is nothing but the splitting operator ∆ introduced in [24] from the requirement of BRST-closedness of integrated vertex operators. Therefore, the Green-Schwarz action (3.17) and its gauge-fixed version yielding the pure spinor model (5.8) provide a simple framework where several accidental features of the pure spinor chiral string become natural.…”

Asymmetrically twisted strings

“…Note also that the twisted string (N = 1) has a natural description in terms of a chiral worldsheet [6,17]. The analysis of the α ′ → ∞ (tensionless) limit yielding the ambitwistor string is very simple [18][19][20].…”

“…The massive states in the bosonic and heterotic cases play the role of auxiliary fields helping to implement higher derivative equations of motion for the massless fields [21,22]. For N > 1, there does not seem to exist a straightforward extension of the chiral map of [17], and the tensionless limit, if sensible, likely becomes more involved. In this case, the higher spin states at mass level N become massless and this investigation might shed some light on the construction of ambitwistor strings for higher spin fields.…”