Nonsupersymmetric Brane/Antibrane Configurations in Type IIA/M-theory

1. Nonsupersymmetric Brane/Antibrane Configurationsin Type IIA/M-theory Masaki Shigemori (Caltech) May 17, 2007 at KITP

2. This talk is based on… • arXiv:0705.0983Joe Marsano, Kyriakos Papadodimas& MS (84 pages!) • Joe gave a preview at KITP in March.This is continuation/supplement

3. metastablenonsusy stablesusy Introduction • Metastable nonsusy configs.in gauge theory / string theory • ISS • Landscape • Pheno./cosmo.

4. D5 S2 __ D5 Introduction • Geometrically induced metastability • Aganagic-Beem-Seo-Vafa • Large N duality • Fluxes softly break N=2  N=0 • Calculational control

5. D4 NS5 NS5 __ D5 D5 S2 __ D4 Introduction • T-dual: IIA/M • IIA side: M-theory lift • Unexplored param. regime in string/M-theory • “Softness” of breaking • Boundary conditions [Bena-Gorbatov-Hellerman-Seiberg-Shih] T

6. Plan of this talk • Introduction • Susy case • Nonsusy curves • “Soft” limit • Boundary conditions

7. Review:Susy Case

8. v=x4+ix5 w=x8+ix9 x6 Type IIA brane construction(a.k.a. Hanany-Witten) NS5 NS5 N D4’s  N=2 U(N) gauge theory with adjoint L

9. D4 v w v w x6  N=1 superpot. Curving NS5 NS5 NS5 D4

10. Gauge theory limit  L System size is substringy

11. Gauge dynamics: M-theory lift [Witten] • NS5 & D4 both lift to M5 • Large gs NG action reliable • M5 curve: • (Relatively) easily obtainedby holomorphicity • SW curve itself! “throat” NS5/D4  M5

12. Strong coupling: M-theory lift • Why does it work?— Power of susy • Scales irrelevant for holomorphic quantities • NG & gauge theorygive same curve

13. When is classical curve really reliable? • As M5 curve (gsÀ1): • Curvature ¿ l11 • Don’t come within l11of self-intersecting • As NS5 + flux (gs¿1): • Curvature ¿ ls • Flux density ¿1/gs • Never met in gauge theory limit 

14. 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

15. Nonsusy Curves

16. D5 S2 __ D5 Nonsusy configurations D4 NS5 [ABSV] NS5 __ D4 IIB IIA Large N dual M-theory lift

17. v w s Harmonic: Virasoro constraint: EOM’s for nonsusy M5 curves • Need to directly solve NG/Polyakov: M lift M5 curve

18. z z=0 Practice 1: simple susy curve v N D4 s M5 log in s:D4’s “pull” NS5 “worldsheet”

19. v w s z z=0 Practice 2: linearly curved NS5’s N D4 “worldsheet”:genus 0

20. v __ N2 D4 Practice 3: simple nonsusy curve N1 D4 • New features: • D4’s and D4’s attract • Need to “hold” back D4’s • D4’s “tilt” in v direction s __

21. Practice 3: simple nonsusy curve • How to get tilted D4 v v rotate s s N D4 rotate log appears in tilted direction

22. __ N2 D4 v s Practice 3: simple nonsusy curve __ • Now combine D4 and D4 parts N1 D4 : determined by Virasoro

23. v s Practice 3: simple nonsusy curve • Virasoro • Force balance • Full nonholo. curve obtained!

24. v w s Practice 4: quadratic curving (“half” of real thing) • Same method works • Full nonholo. curve: • Log bending in s, w • B.C. at ∞ not holomorphic • Minimal distance b/t D4 & D4 NS5 N D4 __ N D4 __

25. v v w w s The real problem • “Worldsheet”: genus 1 • D4’s tilt in w direction w have “logs” N D4 __ N D4

26. The exact curve Im z “worldsheet”  Re z 1 O

27. N D4 v w s __ N D4 The exact curve • Same featuresas the “half” curve: • Log bending in s, w • B.C. at ∞ not holomorphic • Minimal distancebetween D4 & D4 • T-dual won’t even be a complex manifold • Reliable as M5/NS5 curve __

28. The “Soft Limit”

29. 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!

30. D5 S2 D4 NS5 NS5 __ D4 __ D5 “T-duality” T? • Holds more generally • Why work without susy? • There must be some protection • IIB [ABSV]: assuming soft breaking • gsN is controlling “softness”

31. The “soft limit” • Small gsN : consistent with reliability of curve • Why is gsN controlling “softness”? • Tree level  soft • Higher genus candestroy this structure:

32. Boundary Conditions

33. NS5 D6 NS5 D6 Nf-Nc Nf Nc metastablenonsusy NS5’ Nc stablesusy v NS5’ x6 w The issue • ISS vacuum &brane configs: Metastable nonsusy Stable susy

34. NS5 D6 Nf-Nc Nc NS5’ The issue • BGHSS:Boundary conds. different. • Two brane configs are in different theories • One can’t decay into other NS5 D6 Nf Nc NS5’ Metastable nonsusy Stable susy

35. v x6 w 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) __

36. Runaway instability Susy vacuum has been taken to ∞ runaway

37. ? ? ? ? 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

38. 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