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!
