23 August 2013 @ YITP QFT workshop 2013

1

S. Kawamoto (Tunghai U.)

Emission spectrum of soft massless states from heavy superstring

Shoichi Kawamoto (Tunghai Univ. → NCTS, Taiwan )

Phys. Rev. D87 (2013) 124001with T. Matsuo (Anan NCT)

23 August 2013 @ YITP QFT workshop 2013

2

S. Kawamoto (Tunghai U.)

Why heavy (super)string?

Highly excited string is very small, heavy, and unstable

Decay modes, lifetime...?(accessible by perturbation theory)

This decay may be seen as a stringy toy model ofHawking radiation.

e.g. Long-lived states and cosmological application

23 August 2013 @ YITP QFT workshop 2013

3

S. Kawamoto (Tunghai U.)

Blackhole/String correspondnce

Typical size(random walk)

Horizon sizeCorrespondingpoint

[Susskind ('93), Horowitz-Polchinski ('97)]

Highly excited string has enormous entropy

May explain Bekenstein-Hawking entropy?

23 August 2013 @ YITP QFT workshop 2013

4

S. Kawamoto (Tunghai U.)

Decay process

Leading order in gs : Splitting only once

[Dai-Polchinski ('89)]

Not so large momentum transfer: microscopic strings may fly away (soft emission)

“Long” string

“micro” string

Turns out that massless state emission is dominant

23 August 2013 @ YITP QFT workshop 2013

5

S. Kawamoto (Tunghai U.)

Setup

decay

• Observe a heavy string from far away → Averaged initial state• Not observe final states → sum over the possible states• Initial and final states are “heavy”

Rest frame

23 August 2013 @ YITP QFT workshop 2013

6

S. Kawamoto (Tunghai U.)

Decay rate:

averaging sum over A state at level N

Semi-inclusive decay

Exponentially many states at level N → difficult to sum over

(Open superstring) density of states:

23 August 2013 @ YITP QFT workshop 2013

7

S. Kawamoto (Tunghai U.)

projection operator onto level N

Oscillator part is given by 1-loop calc.

[Amati-Russo ('99)]

23 August 2013 @ YITP QFT workshop 2013

8

S. Kawamoto (Tunghai U.)

Note: This tr is not supertrace.

Consider open/closed superstring massless state emissionfrom heavy open/closed superstring.

Boson/fermion massless states

Boson/fermion massless states

Evalueate this trace by use ofGreen-Schwarz superstringin light-cone gauge

Fermion emission is discussed to be subleading effect.

[Iengo-Russo, Chen-Li-She]

23 August 2013 @ YITP QFT workshop 2013

9

S. Kawamoto (Tunghai U.)

Vertex Operators

Light-cone vertex operator:

SUSY

Massless boson emission Massless fermion emission

[Green-Schwarz]

: generator of rotation

23 August 2013 @ YITP QFT workshop 2013

10

S. Kawamoto (Tunghai U.)

Basic traces

integral is easy to carry out.

term survives

1.

2. : large-N factor

23 August 2013 @ YITP QFT workshop 2013

11

S. Kawamoto (Tunghai U.)

Open string state from Open string

Evaluate w-integral by saddle point method

23 August 2013 @ YITP QFT workshop 2013

12

S. Kawamoto (Tunghai U.)

Using, and

Decay rate for open string emission

Thermal distribution of Hagdorn temperature

23 August 2013 @ YITP QFT workshop 2013

13

S. Kawamoto (Tunghai U.)

Closed string emission

from closed

from open

from closed string from open string

Closed string vertex operator: open open

23 August 2013 @ YITP QFT workshop 2013

14

S. Kawamoto (Tunghai U.)

From Heavy closed stringCalculation is factorized

Product of the open result

For example,

Thermal distribution of Hagedorn temp.interpret

23 August 2013 @ YITP QFT workshop 2013

15

S. Kawamoto (Tunghai U.)

Closed states from open string

“Left” and “right” parts of closed vertex act on the same Fock space.

4 vertex insertion

Leading to a bit complicated result...

23 August 2013 @ YITP QFT workshop 2013

16

S. Kawamoto (Tunghai U.)

Example: Boson – Boson case

After v-integral,

In this sum, part gives the dominant contribution.

Leading order part is the same as that from closed string!!

23 August 2013 @ YITP QFT workshop 2013

17

S. Kawamoto (Tunghai U.)

Emission rates (summary)Emission rates:

Open from Open:

Closed from Open/Closed:

23 August 2013 @ YITP QFT workshop 2013

18

S. Kawamoto (Tunghai U.)

Observations IOpen string is like a blackbody.

Behaves like a cavity? (Once absorbed, hardly emitted)

Closed string emission from open/closed string takes the same form.

Locality of the interaction

23 August 2013 @ YITP QFT workshop 2013

19

S. Kawamoto (Tunghai U.)

Blackhole greybody factors

[Harmark-Natario-Schiappa ('07), Kanti-March-Russel(02)]

Greybody factors:s: spin, j: total ang.mon.

: scalar (s=0)

: Dirac fermion

: vector

Dominant j=s modes

blackbody

Spherical BH in an asymptotically flat space

Heavy string

(j=0 ?)

23 August 2013 @ YITP QFT workshop 2013

20

S. Kawamoto (Tunghai U.)

5D D5-D1-KK near extremal BH

[Das-Mathur ('96), Maldacena-Strominger(97)]

[Hosomichi ('97)]

Closed string emission fromHeavy superstring

Bosons

Fermions

Blackhole greybody factors

Why these kinds of black holes?

23 August 2013 @ YITP QFT workshop 2013

21

S. Kawamoto (Tunghai U.)

Summary• Calculate open/closed massless state emission from

heavy open/closed superstring• Open string state emission: blackbody like• Closed string state emission: same for open/closed string• Greybody factors are somehow blackhole like

(Our setup is non-BPS)

● Numerical coefficient?● Next order? Counpling constant vs. large-N