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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