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 landscapeis 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, MEW, particle masses) or of Cosmology ( 10-120 Mp).

If SUSY: CY3X6

M4If 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 V4D() for light fields (fluctuations).

If H=0 in X6SUSY solutions M10= Mink4 CY3

have moduli problem:

V4D() =0

If H0 in X6V

Vol(X6)

runaway potential

To stabilize moduli need `negative energy’ sources, e.g. orientifolds

V

Vol(X6)

So turning on fluxes generically lifts moduli,

but also leads to a huge number of vacua 10500 :

Many cycles in CY3

Many possible quantized values

Closed String Landscape

Anthropic implications? Eg. Cosmological Constant

MPlanck

MPlanck/Nvac

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)

CY3

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):

CY3

D-brane

We will see that all geometric moduli are genericallylifted 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

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 h2,0(S4) holomorphic deformations Xi.

Do they preserve anti-self-duality?

For concreteness, consider a 4-cycle S4 (ie a D7 or a Euclidean D3):

S4 is holomorphic and SUSY

Under a deformation X:

5

S4S4‘

ai (S4‘) = 0automatically if H=0

Generically ai (S4‘) = 0constitute h2,0 equations for h2,0 would-be moduli

Generically solution is a set of isolated points: Open String Landscape -- N exp(h2,0)

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

CY3

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 landscapeis 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!