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 S 2 D5 __ D5 Large N duality Fluxes softly break N=2  Calculational control N=0 4

Introduction  T-dual: IIA/M S 2 D5 __ D5 T NS5 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=x

4

+ix

5

w=x

8

+ix

9

x

6 N D4’s L  N =2 U(N) gauge theory with adjoint  8

Curving NS5 NS5 D4 NS5 D4 v w  N =1 superpot.

v w x

6 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 g s  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 (g s À 1): Curvature ¿

l

11 Don’t come within

l

11 of self-intersecting   As NS5 + flux (g s ¿ 1): Curvature ¿

l

s Flux density ¿ 1/

g

s Never met in gauge theory limit 13

T-duality T-dual S 2 IIA brane construction NS5 in R 6 D4 Tool: M-theory lift 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 S 2 D5 [ABSV] __ D5 NS5 D4 NS5 __ D4 IIB IIA Large N dual M-theory lift 16

EOM ’ s for nonsusy M5 curves

v w

 Need to directly solve NG/Polyakov:

s

M lift Harmonic: M5 curve Virasoro constraint: 17

Practice 1: simple susy curve

v

N D4

s

M5

z

=0 “worldsheet”

z

log in

s

: D4’s “pull” NS5 18

Practice 2: linearly curved NS5 ’ s N D4

v w s z

=0 “worldsheet”: genus 0

z

19

Practice 3: simple nonsusy curve N 1 D4 N 2 __ 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

rotate N D4

s v s

rotate log appears in tilted direction 21

Practice 3: simple nonsusy curve  __ Now combine D4 and D4 parts N 1 D4 N 2 __ D4

v

: determined by Virasoro

s

22

v

Practice 3: simple nonsusy curve  Virasoro Force balance Full nonholo. curve obtained!

s

23

Practice 4: quadratic curving ( “ half ” thing)  of real Same method works NS5  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 v w w s

  “Worldsheet”: genus 1 D4’s tilt in

w



w

direction have “logs” 25

The exact curve Im

z

 “worldsheet” 1 Re

z

O 26

The exact curve

v w s

N D4 __ N D4   Same features as the “half” curve: Log bending in

s, w

B.C. at ∞ not holomorphic Minimal distance between D4 & D4 T-dual won’t even be a complex manifold Reliable as M5/NS5 curve 27

The “Soft Limit”

28

What if

g

s

N

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?

__ D4 S 2 D5 __ D5   Holds more generally Why work without susy?

There must be some protection IIB [ABSV] : assuming soft breaking

g

s

N

is controlling “softness” 30

The “ soft limit ”  Small g s N : consistent with reliability of curve  Why is g s N controlling “softness”?

Tree level  soft Higher genus can destroy this structure: 31

Boundary Conditions

32

The issue  ISS vacuum & brane configs: D6 N f N c N c NS5’ Metastable nonsusy NS5 metastable nonsusy stable susy D6 N f Stable susy NS5

v w x

6 N c NS5’ 33

The issue  BGHSS: Boundary conds. different.

Two brane configs are in different theories One can’t decay into other NS5 NS5 D6 D6 N f N c N c NS5’ N f N c NS5’ Metastable nonsusy Stable susy 34

Nonsusy configs decay  Does not mean our nonsusy config is stable: It decays __ D4/D4 pair annihilate by quantum tunneling (Cf.  -decay in EM field) NS5’s straighten Takes ∞ time (runaway)

v w x

6 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.) 

g

s

N

controls “softness” of breaking Can study string/M landscape in a controlled way  Boundary conditions  Building blocks for model building 38