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

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 An invitation for discussion:

Plan Closed String Landscape Open String Landscape Discussion

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, M EW, particle masses ) or of Cosmology (   M p ).

If SUSY: CY 3 X6X6 M4M4 If homogeneous: dS, AdS or Mink The most basic fact of all: D=4 String theory predicts D=10, so traditional idea is:

Low-energy physics in D=4 obtained from D=10 SUGRA: KK reduction yields V 4D (  ) for light fields (fluctuations). If H=0 in X 6 SUSY solutions M 10 = Mink 4  CY 3 have moduli problem: V 4D (  ) =0

If H  0 in X 6 V Vol(X 6 ) runaway potential To stabilize moduli need `negative energy’ sources, e.g. orientifolds V Vol(X 6 )

So turning on fluxes generically lifts moduli, but also leads to a huge number of vacua  : Many cycles in CY 3 Many possible quantized values Closed String Landscape

Anthropic implications? Eg. Cosmological Constant   M Planck   M Planck /N vac Cf. Weinberg ‘87

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

In the absence of fluxes, D-branes have geometric moduli (massless adjoints in D=4): CY 3 D-brane We will see that all geometric moduli are generically lifted in presence of fluxes, and that an Open String Landscape appears.

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

The SUSY conditions are formally the same w/ or w/o fluxes, but their solutions are very different Consider a SUSY solution. There are h 2,0 (S 4 ) holomorphic deformations X i. Do they preserve anti-self-duality? For concreteness, consider a 4-cycle S 4 (ie a D7 or a Euclidean D3): S 4 is holomorphic and SUSY

Under a deformation X: 55 S4S4 S4‘S4‘ a i (S 4 ‘) = 0 automatically if H=0 Generically a i (S 4 ‘) = 0 constitute h 2,0 equations for h 2,0 would-be moduli Generically solution is a set of isolated points: Open String Landscape -- N  exp(h 2,0 )

One immediate application: D-brane instantons Reduced number of bosonic zero-modes Reduced number of fermionic zero-modes New instantons may contribute to D=4 superpotential CY 3 D-brane

Discussion Important caveat: Closed Landscape far from established (cf. Tom Banks) 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? Message: Scientific Issue, not taste

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!