Download Unruh Effect in Closed String Theory

Unruh Effect in Closed String Theory
Hokkaido Univ.
Kenji Hotta
1. Introduction

Hawking-Unruh Effect
quantum field theory in curved space-time
Hawking radiation
Black holes emit thermal radiation.
information loss paradox
Unruh effect
Accelerated observers experience a thermal bath.

Unruh Effect in String Theory
We need to handle second quantized strings.
Unruh effect in open bosonic string field theory
Hata-Oda-Yahikozawa
closed strings can propagate bulk curved space-time
Unruh effect in closed string theory bosonic
super
light-cone gauge closed string Kaku-Kikkawa
Contents
1.
2.
3.
4.
5.
6.
Introduction 
Space-time Coordinates
Closed Strings in Minkowski Space-time
Closed Strings in Rindler Space-time
Unruh Effect in Closed String Theory
Conclusion and Discussion
2. Space-time Coordinates
Minkowski coords.
Rindler coords. (right Rindler wedge)
Fixed
lines represent
constant acceleration
Light-cone coords.
Light-cone like coords.
relation between two coords.
3. Closed Strings in Minkowski Space-time

Light-Cone Gauge Closed Bosonic String Field
We consider free string
eq. of motion
mode expansion
cf) Kaku-Kikkawa
solution
The wave function
is also the solution of the equation of motion.
The factor
plays a role of phase shift.
This wave function also satisfies the Klein-Gordon eq.
Let us expand
as
second quantization
Minkowski vacuum
4. Closed Strings in Rindler Space-time

Light-Cone Gauge in Rindler Space-time
cf) first quantized string case
de Vega-Sanchez
eq. of motion
cf) massive scalar particle case
wave function
satisfies
In the solution,
and
are non-constant.
We can not choose light-cone gauge.

Klein-Gordon Equation in Rindler Space-time
We have already obtained the solution of Klein-Gordon eq.
in Minkowski Space-time.
If we can represent the solution of Klein-Gordon eq.
in Rindler space-time by the combination of the solutions of
Klein-Gordon eq. in Minkowski space-time, it would be OK!
Minkowski
Rindler (right Rindler wedge)
solution (right Rindler wedge)
We can expand the field
second quantization
as
5. Unruh Effect in Closed String Theory
expansions of solution
Minkowski
Rindler
Bogoliubov transformation
This is Bose-Einstein spectrum for radiation
at temperature
.
6. Conclusion and Discussion

Unruh Effect in Closed Bosonic String Theory
We argued Unruh effect in the case of closed bosonic strings
based on light-cone gauge SFT.
We obtain Bose-Einstein spectrum for radiation
at temperature
.
For the superstring case, we obtain Bose-Einstein spectrum
and Fermi-Dirac one for radiation at temperature
.

Relation to Brane-antibrane Case
Can we identify left wedge part as open strings
and brane-antibrane pairs?

Information Loss Paradox in Black Hole Physics
How to resolve this problem in string theory?