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Thermodynamics and Cosmological Constant of Non-Local Field Theories from p-Adic Strings. Joe Kapusta* University of Minnesota. *Based on: PRL 104 , 021601 (2010), arXiv:1005.0430 and arXiv:1006.4098 with T. Biswas and J .A. R. Cembranos. Wikipedia.

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thermodynamics and cosmological constant of non local field theories from p adic strings

Thermodynamics and Cosmological Constant of Non-Local Field Theories from p-Adic Strings

Joe Kapusta*

University of Minnesota

*Based on: PRL 104, 021601 (2010), arXiv:1005.0430 and arXiv:1006.4098

with T. Biswas and J .A. R. Cembranos.

slide2

Wikipedia

In mathematics, and chiefly number theory, the p-adic number system

for any prime number p extends the ordinary arithmetic of the rational

numbers in a way different from the extension of the rational number

system to the real and complex number systems. The extension is

achieved by an alternative interpretation of the concept of absolute value.

  • String Theories over p-adic Fields*
  • Quantum fields valued in the field of complex numbers
  • Space-time coordinates valued in the field of real numbers
  • World-sheet coordinates valued in the field of p-adic numbers
  • *Freund & Olson (1987), Freund & Witten (1987)
slide3

The N-point tree amplitudes of the open string can be

generated from a non-local Lagrangian of a single scalar

field (the tachyon) which has a tachyon-free vacuum with

no particles but with soliton solutions.

open string coupling prime number string tension

Brekke, Freund, Olson & Witten (1988); Frampton & Okada (1988)

key results
Key Results
  • There are no particle degrees of freedom so there is no one-loop contribution to the partition function
  • The lowest order contribution arises from interactions
  • A counter-term must be added to avoid the appearance of a ghost in a loop expansion which has the consequence that …
  • The vacuum energy is positive and hierarchically suppressed
  • Perturbation theory breaks down at a temperature of order
  • Soliton solutions exist at all temperatures and become important when
slide5

Rescale the fields to put the action in the form

with dimensionful coupling constant

and non-local propagator

slide8

Thermal Duality:

  • Analogous to dualities found in stringy calculations
  • Does not hold at higher order
  • Leads to peculiar thermodynamics
  • Ghost appears due to self-energy
slide9

vacuum energy:

low T:

no particle degrees

of freedom

high T:

slide10

Necklace diagrams

and sunset diagrams

can be evaluated. They become comparable in

magnitude to lower order diagrams when

planck mass cosmological constant
Planck Mass & Cosmological Constant

volume of extra-dimensional compactified space

hierarchical suppression

known dimensionless function of p

solitons at finite temperature
Solitons at Finite Temperature

Soliton solutions in Euclidean space at zero temperature

were found by Brekke, Freund, Olson & Witten (1988).

conclusions
Conclusions
  • We studied a nonlocal field theory arising from
  • string theory at finite temperature.
  • The theory has no particle degrees of freedom.
  • Pertubation theory is accurate up to and beyond
  • the string scale when the string coupling is weak.
  • There is a positive cosmological constant and
  • power-law behavior at high temperature.
  • Soliton solutions were found at all temperatures.

Supported by the U.S. Department of Energy under Grant No. DE-FG02-87ER40328.