Exact TT[over ¯] Deformation of Two-Dimensional Maxwell Theory

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• String Theory

Background:

• The partition function is crucial for understanding quantum field theories.
• TT[over ¯] deformation offers a novel way to study integrable models.
• Two-dimensional Maxwell theory provides a tractable framework for exploring quantum phenomena.

Purpose of the Study:

• To determine the partition function of TT[over ¯]-deformed two-dimensional Maxwell theory.
• To investigate the impact of the deformation parameter μ on the theory's spectrum and behavior.
• To explore the nature of quantum phase transitions in this deformed theory.

Main Methods:

• Solving the relevant flow equation at the level of individual flux sectors.
• Exactly summing the "instanton" series.
• Analyzing the partition function at arbitrary values of μ.

Main Results:

• A well-defined expression for the partition function was obtained.
• For μ>0, spectrum truncation and infinite-order quantum phase transitions were observed, linked to vanishing Polyakov-loop correlators.
• For μ<0, nonperturbative contributions significantly altered the partition function's structure.

Conclusions:

• The TT[over ¯] deformation leads to distinct physical behaviors depending on the sign of μ.
• The study provides insights into quantum phase transitions and nonperturbative effects in deformed 2D quantum field theories.