[Paper Review] Supercritical N = 2 string theory

Simeon Hellerman, Ian Swanson|ArXiv.org|Sep 13, 2007

Black Holes and Theoretical Physics14 references17 citations

TL;DR

This paper investigates supercritical N=2 string theory in dimensions above the critical D=4, using a linear dilaton background to show that only one physical time dimension remains, unlike the two timelike directions in the critical D=4 case. It demonstrates exact solutions for dynamical dimensional reduction and transitions from N=2 to bosonic string theory via closed-string tachyon condensation, establishing a precise embedding of the bosonic string within the N=2 vacuum space and confirming exact solvability through BRST quantization.

ABSTRACT

The N=2 string is examined in dimensions above the critical dimension (D=4) in a linear dilaton background. We demonstrate that string states in this background propagate in a single physical time dimension, as opposed to two such dimensions present when the dilaton gradient vanishes in D=4. We also find exact solutions describing dynamical dimensional reduction and transitions from N=2 string theory to bosonic string theory via closed-string tachyon condensation.

Motivation & Objective

• To analyze the N=2 string theory in supercritical dimensions (D > 4) using a linear dilaton background.
• To resolve the structure of physical time directions in the theory, showing only one remains physical.
• To construct exact solutions describing dynamical dimensional reduction via tachyon condensation.
• To demonstrate a c-duality transition from N=2 string theory to purely bosonic string theory.
• To explicitly embed the bosonic string within the solution space of N=2 string vacua.

Proposed method

• The study employs a linear dilaton background to break conformal invariance and analyze the N=2 string in D > 4 spacetime dimensions.
• It uses BRST quantization to derive physical states and constraints, particularly focusing on the super-Virasoro algebra and R-symmetry conditions.
• The authors analyze tachyon condensation in the worldsheet theory, treating holomorphic tachyons as superpotential terms.
• They derive exact solutions for transitions by solving the equations of motion in the presence of a tachyon condensate that nucleates a bubble of new vacuum.
• The bosonic string embedding is constructed via explicit variable redefinitions that map the N=2 theory to a bosonic string limit.
• The BRST current is explicitly transformed using similarity transformations to verify consistency of the embedding at tree level.

Experimental results

Research questions

• RQ1 How many physical time dimensions are present in supercritical N=2 string theory in a linear dilaton background?
• RQ2 What is the role of R-symmetry in eliminating one of the two timelike directions present in the critical D=4 case?
• RQ3 Can tachyon condensation in the N=2 string lead to a dynamical reduction of spacetime dimensions?
• RQ4 Does the N=2 string theory admit a c-duality transition to purely bosonic string theory via tachyon condensation?
• RQ5 How can the bosonic string be embedded within the vacuum space of the N=2 string theory?

Key findings

• Only one physical time dimension remains in supercritical N=2 string theory in a linear dilaton background, due to R-symmetry constraints eliminating one timelike direction.
• Exact solutions are found for dynamical dimensional reduction, where n spatial dimensions are quenched via tachyon condensation.
• The theory exhibits a c-duality transition to purely bosonic string theory through closed-string tachyon condensation, breaking worldsheet supersymmetry.
• The bosonic string is explicitly embedded in the N=2 vacuum space via a specific variable redefinition that maps the N=2 theory to the bosonic limit.
• BRST quantization confirms the consistency of the embedding at tree level, with exact solvability preserved through quantum corrections.
• Quantum corrections to the dilaton gradient and string-frame metric exactly compensate for central charge loss from dimension reduction, preserving consistency.