Finite-temperature string theory and twisted tori

Journal Article · Fri Jul 15 04:00:00 EDT 1988 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.38.552· OSTI ID:6989315

McGuigan, M

We show that the introduction of a finite temperature into string theory is mathematically equivalent to compactifying the timelike coordinate on a twisted torus of radius ..beta../2..pi.. = 1/2..pi..kT, the reciprocal of the temperature. We derive a general formula for the one-loop vacuum amplitude ..lambda..(..beta..) of a string theory compactified on a twisted torus that is manifestly modular invariant and is almost as easy to apply as in the compactification of a string theory on an ordinary torus. The connection with statistical mechanics is made through the formula lnZ(..beta..) = -..beta..V..lambda..(..beta..) where Z(..beta..) is the partition function and V the volume of the system. We discuss how the function sigma(E) which counts the number of string states of total energy E and plays a central role in the microcanonical ensemble can be computed by taking the inverse Laplace transform of Z(..beta..) and we give estimates of sigma(E) for low and high energy densities by this method. We study the effect of finite temperature on the effective potentials for different parameters which determine a string theory's compactification. As supersymmetry is broken at finite temperature these potentials are nontrivial. We study the effect of finite temperature on the Wilson loop mechanism for gauge symmetry breaking and find that for a supersymmetric theory compactified on a torus finite-temperature effects favor the trivial vacuum. Also the effective potential for the radius R of the torus becomes modified so as to be minimum at R = 0 or R = infinity. The introduction of interactions and curvature effects into our formalism is discussed.

• Research Organization: The Rockefeller University, 1230 York Avenue, New York, New York 10021
• OSTI ID: 6989315
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 38:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
ENERGY DENSITY
EXTENDED PARTICLE MODEL
FUNCTIONS
GAUGE INVARIANCE
INTEGRAL TRANSFORMATIONS
INVARIANCE PRINCIPLES
LAPLACE TRANSFORMATION
MATHEMATICAL MODELS
MECHANICS
PARTICLE MODELS
PARTITION FUNCTIONS
QUARK MODEL
STATISTICAL MECHANICS
STRING MODELS
SUPERSYMMETRY
SYMMETRY
SYMMETRY BREAKING
TEMPERATURE DEPENDENCE
TORI
TRANSFORMATIONS
VACUUM STATES
WILSON LOOP