Open Landscape David Mateos University of California at Santa Barbara

1. Open Landscape David Mateos University of California at Santa Barbara (work with Jaume Gomis and Fernando Marchesano)

2. An invitation for discussion: Landscape ideas naturally lead to some anthropic reasoning And a warning for the skeptics: “A physicist talking about the landscape is like a cleric talking about pornography: No matter how much you say you’re against it, some people will think you’re a little too interested! S. Weinberg

3. Plan Closed String Landscape Open String Landscape Discussion

4. String Theory • Achieves unification of GR and QM. • Has resolved important problems in quantum GR such as BH entropy, and contains many features of the SM. • However, not a single sharp prediction, and no real understanding of the basic facts of SM (gauge group, number of generations, MEW, particle masses) or of Cosmology ( 10-120 Mp).

5. X6 M4 The most basic fact of all: D=4 String theory predicts D=10, so traditional idea is: If SUSY: CY3 If homogeneous: dS, AdS or Mink

6. Low-energy physics in D=4 obtained from D=10 SUGRA: KK reduction yields V4D() for light fields (fluctuations). SUSY solutions M10= Mink4 CY3 have moduli problem: V4D() =0 If H=0 in X6

7. If H0 in X6 runaway potential V To stabilize moduli need `negative energy’ sources, e.g. orientifolds Vol(X6) V Vol(X6)

8. Many cycles in CY3 Many possible quantized values So turning on fluxes generically lifts moduli, but also leads to a huge number of vacua  10500 : Closed String Landscape

9. Anthropic implications? Eg. Cosmological Constant   MPlanck  MPlanck/Nvac Cf. Weinberg ‘87

10. Open strings are part of the spectrum Important for model building (eg SM fields live on D-branes) SU(3)  SU(2)  U(1) CY3 Generate non-perturbative effects (eg D-brane instantons) D-brane Generate large hierarchies (apps. to particle physics, cosmic strings,etc.) D-branes Essential to study SUSY D-branes in this setup because:

11. In the absence of fluxes, D-branes have geometric moduli (massless adjoints in D=4): CY3 D-brane We will see that all geometric moduli are generically lifted in presence of fluxes, and that an Open String Landscape appears.

12. A The combination that enters the action is: NS 2-form (potential for H ) [ A] Recall that on a D-brane there is a U(1) gauge field:

13. S4 is holomorphic and SUSY The SUSY conditions are formally the same w/ or w/o fluxes, but their solutions are very different For concreteness, consider a 4-cycle S4 (ie a D7 or a Euclidean D3): Consider a SUSY solution. There are h2,0(S4) holomorphic deformations Xi. Do they preserve anti-self-duality?

14. ai (S4‘) = 0 automatically if H=0 5 Generically solution is a set of isolated points: Open String Landscape -- N exp(h2,0) S4‘ S4 Under a deformation X: Generically ai (S4‘) = 0 constitute h2,0 equations for h2,0 would-be moduli

15. Reduced number of fermionic zero-modes New instantons may contribute to D=4 superpotential CY3 D-brane One immediate application: D-brane instantons Reduced number of bosonic zero-modes

16. Discussion Open Landscape appears on top of each Closed Vacuum Implications for phenomenology, model building, etc. How about Wilson Line Moduli? In T-dual picture Wilson Lines are stabilized. T-dual naturally leads to twisted tori. How about non-geometric flux compactitifcations? Important caveat: Closed Landscape far from established (cf. Tom Banks) Message: Scientific Issue, not taste

17. Conclusion “A physicist talking about the landscape is like a cleric talking about pornography: No matter how much you say you’re against it, some people will think you’re a little too interested!” S. Weinberg By now you’re all in trouble!