Path Integral Equivalence between Super D-string and IIB Superstring

TL;DR

This paper demonstrates the exact path integral equivalence between the super D-string and IIB Green-Schwarz superstring actions, revealing implications for fermionic constraints and SL(2,Z) covariant tensions.

Contribution

It establishes a precise equivalence between super D-string and IIB superstring actions, including the role of the theta term and electric field quantization effects.

Findings

Super D-string action is equivalent to IIB superstring with a theta term.

Fermionic constraint issues are inherited from the IIB superstring.

Quantized electric field leads to SL(2,Z) covariant tension.

Abstract

We show that the super D-string action is exactly equivalent to the IIB Green-Schwarz superstring action with some "theta term" in terms of the path integral. Since the "theta term" imposes the Gauss law constraint on the physical state but contributes to neither the mass operator nor the constraints associated with the kappa symmetry and the reparametrization, this exact equivalence implies that the impossibility to disentangle the first and second class fermionic constraints covariantly in the super D-string action is generally inherited from the IIB Green-Schwarz superstring action except specific gauge choices which make the ground state massive, such as the static gauge. Moreover, it is shown that if the electric field is quantized to be integers, the super D-string action can be transformed to the IIB Green-Schwarz superstring action with $SL(2, Z)$ covariant tension.