Small Black Ring

Report
Nonsupersymmetric
Brane/Antibrane Configurations
in Type IIA/M-theory
Masaki Shigemori (Caltech)
May 17, 2007 at KITP
1
This talk is based on…

arXiv:0705.0983
Joe Marsano, Kyriakos Papadodimas
& MS (84 pages!)

Joe gave a preview at KITP in March.
This is continuation/supplement
2
Introduction

Metastable nonsusy configs.
in gauge theory / string theory
ISS
Landscape
Pheno./cosmo.
metastable
nonsusy
stable
susy
3
Introduction

Geometrically induced metastability
Aganagic-Beem-Seo-Vafa
S2
D5
__
D5
Large N duality
Fluxes softly break N=2  N=0
Calculational control
4
Introduction

T-dual: IIA/M
NS5
S2
D5
__
D5
T
D4
NS5
__
D4
IIA side: M-theory lift
Unexplored param. regime in string/M-theory
“Softness” of breaking
Boundary conditions [Bena-Gorbatov-Hellerman-Seiberg-Shih]
5
Plan of this talk

Introduction

Susy case

Nonsusy curves

“Soft” limit

Boundary conditions
6
Review:
Susy Case
7
Type IIA brane construction
(a.k.a. Hanany-Witten)
NS5
NS5
v=x4+ix5
w=x8+ix9
N D4’s
L
x6
 N=2 U(N) gauge theory
with adjoint 
8
Curving NS5
D4
NS5
D4
NS5
v
w
 N=1 superpot.
v
w
x6
9
Gauge theory limit

L
System size is substringy
10
Gauge dynamics: M-theory lift [Witten]


“throat”
NS5/D4  M5

NS5 & D4 both lift to M5
Large gs
 NG action reliable
M5 curve:
(Relatively) easily obtained
by holomorphicity
SW curve itself!
11
Strong coupling: M-theory lift

Why does it work?
— Power of susy
Scales irrelevant for
holomorphic quantities
NG & gauge theory
give same curve
12
When is classical curve really reliable?

As M5 curve (gsÀ1):
Curvature ¿ l11
Don’t come within l11
of self-intersecting


As NS5 + flux (gs¿1):
Curvature ¿ ls
Flux density ¿1/gs

Never met in gauge
theory limit
13
T-duality
T-dual
IIA brane construction
NS5 in R6
D4
Tool: M-theory lift

S2
IIB geom. engineering
Noncpt. CY (ALE fibr.)
D5
Tool: large N duality
Why work? — power of susy
Scales irrelevant
Without susy, not expected to work, a priori
14
Nonsusy Curves
15
Nonsusy configurations
[ABSV]
S2
D5
NS5
__
D5
IIB
Large N dual
D4
NS5
__
D4
IIA
M-theory lift
16
EOM’s for nonsusy M5 curves

v w
Need to directly solve
NG/Polyakov:
s
Harmonic:
M lift
M5 curve
Virasoro constraint:
17
Practice 1:
simple susy curve
v
N D4
s
M5
z
z=0
“worldsheet”
log in s:
D4’s “pull” NS5
18
Practice 2:
linearly curved NS5’s
N D4
v
w
s
z
z=0
“worldsheet”:
genus 0
19
Practice 3:
simple nonsusy curve
N1 D4
__
N2 D4

v
s
New features:
__
D4’s and D4’s attract
Need to “hold” back D4’s
D4’s “tilt” in v direction
20
Practice 3:

simple nonsusy curve
How to get tilted D4
v
N D4
rotate
v
s
s
rotate
log appears in tilted direction
21
Practice 3:

simple nonsusy curve
__
Now combine D4 and D4 parts
N1 D4
__
N2 D4
v
: determined by Virasoro
s
22
Practice 3:

simple nonsusy curve
Virasoro
Force balance
v
s
Full nonholo. curve obtained!
23
Practice 4:
quadratic curving (“half” of real
thing)

NS5

Same method works
Full nonholo. curve:
N D4
__
N D4
v
w
s
Log bending in s, w
B.C. at ∞ not holomorphic __
Minimal distance b/t D4 & D4
24
The real problem
N D4
__
N D4
v w
v
w
s


“Worldsheet”: genus 1
D4’s tilt in w direction
 w have “logs”
25
The exact curve
Im z

O
“worldsheet”
1
Re z
26
The exact curve

Log bending in s, w
N D4
B.C. at ∞ not holomorphic
Minimal distance
__
between D4 & D4
__
N D4
v w
Same features
as the “half” curve:
T-dual won’t even be a
complex manifold
s

Reliable as M5/NS5 curve
27
The “Soft Limit”
28
What if gsN is small?

Take
in the exact curve:
Tilting vanishes
v, w : holomorphic, s : harmonic
Corresponds to exact min. of IIB potential
: unexpected!
29
“T-duality”
NS5
D4
NS5
T?
S2
D5
__
D5
__
D4


Holds more generally
Why work without susy?
There must be some protection
IIB
[ABSV]:
assuming soft breaking
gsN is controlling “softness”
30
The “soft limit”

Small gsN : consistent with reliability of curve

Why is gsN controlling “softness”?
Tree level  soft
Higher genus can
destroy this structure:
31
Boundary Conditions
32
The issue

ISS vacuum &
brane configs:
metastable
nonsusy
stable
susy
NS5
D6
Nf-Nc
Nc
NS5
D6
w
Nf
NS5’
Metastable nonsusy
v
x6
Nc
NS5’
Stable susy
33
The issue

BGHSS:
Boundary conds. different.
Two brane configs are in different theories
One can’t decay into other
NS5
D6
Nf-Nc
Nc
NS5
D6
Nf
NS5’
Metastable nonsusy
Nc
NS5’
Stable susy
34
Nonsusy configs decay

Does not mean our nonsusy config is stable:
It decays
v
x6
w
__
D4/D4 pair annihilate by quantum tunneling
(Cf. -decay in EM field)
NS5’s straighten
Takes ∞ time (runaway)
35
Runaway instability
Susy vacuum has
been taken to ∞
runaway
36
Relevance of nonsusy brane configs


Gauge theory is approximation of string 
Embed in compact CY:
BC arises from dynamics of “the rest”
?
?
?
?
In the whole sys, runaway ends
Local “building block” for model building
37
Conclusions

M5/NS5 curve:
Can explore nonsusy landscape of string/M-theory
Can be easily generalized (ADE, etc.)

gsN controls “softness” of breaking
Can study string/M landscape in a controlled way

Boundary conditions

Building blocks for model building
38

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