Green-Schwarz and pure spinor formulations of chiral strings

Abstract

Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the Oda-Tonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.

Remarks on the critical dimension of left-handed string and its quasiconformal nature

“…such that the critical dimension does not depend on β, which agrees with [3][4][5][6][7][8][9]. 3 Without the obstruction of the existence of critical dimension, the scattering amplitude of left-handed string is effectively valid in arbitrary dimension; one can do the z-integral such that the remaining conformal fields of left-handed string (correpongding to z) are completely decoupled.…”

“…From now on, we use the term "left-handed string" to refer to the string with both changed boundary conditions and singular limit, whereas the "chiral string" stands for the string with only the change of boundary conditions. Further calculations ( [3][4][5][6][7][8][9]) also show that it is almost obvious that the corresponding critical dimension of chiral string is the same as its conventional counterpart in string theory.…”

Taming the 11D pure spinor b-ghost

“…More interestingly, the kinematic numerators at any multiplicity were found to be proportional to nested b-ghost expressions, and to match the multiparticle superfields constructed in [18] up to generalized gauge transformations and BRST-exact terms. These computations were possible to be methodically carried out due to the existence of simpler alternative expressions for the 10D b-ghost [19][20][21]. Such expressions make use of negative ghost number operators, referred to as physical operators, satisfying a set of defining relations resembling the 10D super-Yang-Mills equations of motion at linearized order.…”