[Paper Review] Thermal Supersymmetry in Thermal Superspace

Cláudio L. Lucchesi|ArXiv.org|Aug 27, 1998

Quantum Mechanics and Non-Hermitian Physics3 citations

TL;DR

This paper introduces a thermal supersymmetry framework within thermal superspace, where Grassmann variables are time-dependent and antiperiodic in imaginary time with inverse-temperature periodicity. It formulates a 'super-KMS' condition for superfield propagators, constructs thermal covariant derivatives and chiral/antichiral superfields, and derives a thermal supersymmetry algebra identical in structure to the zero-temperature case, while identifying thermal supersymmetry breaking via mass degeneracy lifting and non-invariant thermal actions.

ABSTRACT

Thermal superspace is characterized by Grassmann variables which are time-dependent and antiperiodic in imaginary time, with a period given by the inverse temperature. The thermal superspace approach allows to define thermal superfields obeying consistent boundary conditions and to formulate a ``super-KMS'' condition for superfield propagators. Upon constructing thermal covariantizations of the superspace derivative operators, we define thermal covariant derivatives and provide a definition of thermal chiral and antichiral superfields. Thermal covariantizations of the generators of the super-Poincaré algebra are also constructed, and the thermal supersymmetry algebra is computed; it has the same structure as at T=0. We then investigate realizations of this thermal supersymmetry algebra on systems of thermal fields. In doing so, we observe thermal supersymmetry breaking in terms of the lifting of the mass degeneracy, and of the non-invariance of the thermal action.

Motivation & Objective

• To extend supersymmetry to finite temperature using a thermal superspace formalism with time-dependent, antiperiodic Grassmann variables.
• To define consistent boundary conditions for thermal superfields and formulate a 'super-KMS' condition for propagators.
• To construct thermal covariant derivatives and define thermal chiral and antichiral superfields.
• To derive the thermal supersymmetry algebra and investigate its structure and invariance properties.
• To analyze thermal supersymmetry breaking through mass degeneracy lifting and non-invariant thermal actions.

Proposed method

• Introduce thermal superspace with Grassmann variables that are antiperiodic in imaginary time with period β = 1/T.
• Define thermal covariant derivatives by covariantizing standard superspace derivative operators under thermal conditions.
• Construct thermal chiral and antichiral superfields using the thermal covariant derivatives.
• Derive the thermal supersymmetry algebra by covariantizing the generators of the super-Poincaré algebra.
• Apply the formalism to systems of thermal fields to examine symmetry realization and breaking.
• Use the 'super-KMS' condition to ensure consistent thermal behavior of superfield propagators.

Experimental results

Research questions

• RQ1 How can supersymmetry be consistently formulated at finite temperature using a superspace formalism with time-dependent Grassmann variables?
• RQ2 What is the structure of the thermal supersymmetry algebra, and does it retain the same form as at zero temperature?
• RQ3 How do thermal superfields and their propagators satisfy boundary conditions consistent with finite-temperature field theory?
• RQ4 In what ways does thermal supersymmetry break, and how can this be detected in thermal field systems?
• RQ5 Can a 'super-KMS' condition be defined for superfield propagators that generalizes the standard KMS condition to supersymmetric theories?

Key findings

• The thermal supersymmetry algebra retains the same structure as at zero temperature, indicating no modification to the underlying algebraic relations.
• Thermal covariant derivatives are successfully constructed, enabling a consistent formulation of chiral and antichiral superfields at finite temperature.
• The 'super-KMS' condition is defined for superfield propagators, ensuring consistency with thermal boundary conditions in imaginary time.
• Thermal supersymmetry breaking is observed through the lifting of mass degeneracy between bosonic and fermionic states.
• The thermal action is found to be non-invariant under thermal supersymmetry, signaling explicit breaking in the effective action.
• The formalism provides a consistent framework for studying supersymmetric field theories at finite temperature using thermal superspace techniques.