Holomorphic Anomaly Mediation

Yu Nakayama (Caltech)arXiv:1009.0543 and to appear

SUSY breaking

Typically SUSY breaking effect is mediated via non-renormalizable higher dimensional operators

In particular, gravity, moduli, anomaly mediation is essentially gravitational. So, we may learn important clues about the fundamental theory including gravity (hopefully string theory)

Even gauge mediation may admit gravity dual.

Anomaly mediation• Gauge coupling constant in string theory (Kaplunov

sky-Louis formula)

• Gauge induced Weyl-Kahler-Sigma model anomaly• Corresponding gaugino mass formula

• The last three terms from F-terms of matter. The first term from conformal compensator (gravitational F-term).

• Claimed to be universal…

No anomaly mediation in string theory?

• Only a limited number of literatures… (Antoniadis-Taylor, Conlon-Goodsell-Palti)

• Explicit computation in Sherk-Schwarz compactification gave

with no anomaly mediation effects.

• Typically, the last three-terms cancel (cancellation of anomaly?)

and the gravitational breaking is zero (no-scale)…

• We’d like to study contribution in the gaugino mass from string theory.

• Deeply (quantum) gravitational.• Nevertheless, we can compute it by using

refined topological string theory.• Contribution only comes from holomorphic

anomaly and can be evaluated by the refined holomorphic anomaly equation

• As universal as the anomaly mediation

Objectives of my talk

Refined topological string amplitudes

Topological string and N=1,2 compactification

• Consider type II string theory to compute

• Graviphoton insertion Topological twist

• SUSY breaking by flux N=1 superpotential

Refined topological string amplitude in N=2

SUSY breaking by flux gives higherderivative F-terms (can be D-terms):

g = 0, n= 1 example:

Generate gaugino mass

Refined topological string amplitude in N=1

So, we learned thatnon-holomorphic terms in refined topological string amplitude

s generategaugino mass

Holomorphic anomaly mediation

Computation of refined topological string amplitudes

and gaugino mass

Two conjectures:1. Antoniadis et al: For specific choice of ve

ctor multiplet, one can compute the Nekrasov partition function:

2. Krefl-Walcher: Nekrasov partition function satisfies the extended holomorphic anomaly equation:

How to compute refined topological amplitudes 1

1. Extended holomorphic anomaly equation relates:

2. Furthermore, one loop extended holomorphic anomaly equation is integrable:

3. So without any ambiguity, we can compute the universal gaugino mass

How to compute refined topological amplitudes 2

How to compute refined topological amplitudes 3

1. Mass of the other gauginos are related by the holomorphic anomaly.

2. We know that for the universal gaugino (S),

3. Supersymmetry demands the “refined holomorphic anomaly equation”:

4. Mass mixing can also be determined from

Some phenomenology

Holomorphic anomaly mediation generically predicts split supersymmetry

• Sfermion mass comes from gravity/moduli mediation:

• Sequestering/no-scale. Sfermion mass comes from anomaly mediation:

3. Anomaly mediation in sfermion sector may vanish…

Conclusion

New developments in string theory makes “higher gravitational amplitudes” computable.

It is exciting to see holomorphic anomaly at collider experiments.