Open Superstring on Symmetric Product

TL;DR

This paper explores the second-quantized open superstring theory on symmetric products, deriving fermionic partition functions, constructing boundary states, and confirming the SO(32) gauge group requirement for anomaly cancellation.

Contribution

It extends the symmetric product framework to open superstrings, providing new fermionic partition functions and classifying boundary states in terms of long string language.

Findings

Fermionic partition functions derived from twisted boundary conditions.

Boundary states classified into three types based on topology changes.

SO(32) gauge group confirmed for anomaly cancellation.

Abstract

The string theory on symmetric product describes the second-quantized string theory. The development for the bosonic open string was discussed in the previous work. In this paper, we consider the open superstring theory on the symmetric product and examine the nature of the second quantization. The fermionic partition functions are obtained from the consistent fermionic extension of the twisted boundary conditions for the non-abelian orbifold, and they can be interpreted in terms of the long string language naturally. In the closed string sector, the boundary/cross-cap states are also constructed. These boundary states are classified into three types in terms of the long string language, and explain the change of the topology of the world-sheet. To obtain the anomaly-free theory, the dilaton tadpole must be cancelled. This condition gives SO(32) Chan-Paton group as ordinary superstring theory.