G. Pradisi - Non-perturbative... Non-perturbative transitions among intersecting brane vacua Gianfranco Pradisi Universita' di Roma “Tor Vergata” and INFN Sezione di Roma “Tor Vergata” C. Angelantonj, C. Condeescu, E. Dudas, G.P., arXiv:1105.3465 [hep-th] Stockholm, june 10th, 2011 NORDITA Nordic Institute for Theoretical Physics
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G. Pradisi - Non-perturbative...
Non-perturbative transitions among
intersecting brane vacua
Gianfranco Pradisi
Universita' di Roma “Tor Vergata” and
INFN Sezione di Roma “Tor Vergata”
C. Angelantonj, C. Condeescu, E. Dudas, G.P., arXiv:1105.3465 [hep-th]
Stockholm, june 10th, 2011
NORDITA Nordic Institute for Theoretical Physics
G. Pradisi - Non-perturbative...
OUTLINE
Brane Recombination
Geometry
6-d Supersymmetric vacua
6-d BSB vacua
Recombination vs Higgsing
Recombination in the bulk: the effective potential
Stability of BSB vacua under recombination
Classical solutions and brane transmutation
4-d examples
Conclusions
G. Pradisi - Non-perturbative...
Brane Recombination
Homology of the two-torus
Orientifolds
Intersection form
for a four-torus
D.Cremades
L. Ibanez
F. Marchesano
M. Cvetic
G. Shiu
A. Uranga
R. Blumenhagen
L. Goerlich
T. Ott
G. Pradisi - Non-perturbative...
Orbifold homology
bulk 2-cycles
Intersection form
exceptional (collapsed) 2-cycles
localized at the fixed points
A generic 2-cycle
fractional
2-cycles
D.Diaconescu
M. Douglas (1997)
J. Gomis
G. Pradisi - Non-perturbative...
Susy orientifold vacua
2-cycles wrapped by O7-planes
We focus on factorizable cycles
complex charges
Invariant cycles where
A vacuum is determined by the wrapping numbers
and (at least) one crossed fixed point (the origin)
G. Pradisi - Non-perturbative...
Reps and Multiplicities of charged hypermultiplets in T4/Z2
Stack a The intersection numbers determine the multiplicities
G. Pradisi - Non-perturbative...
Tadpole cancellation conditions
untwisted
Twisted (automatic)
Brane Recombination
(RR charge conservation)
Example: U(16) x U(16) [BSGP] modelM. Bianchi
A. Sagnotti (1990)
E. Gimon
J. Polchinski (1996)
G. Pradisi - Non-perturbative...
(Partial) recombination to a single additional factorizable stack
A first solution: complete brane recombination
R. Blumenhagen
V. Braun
B. Koers (2002)
D. Luest
G. Pradisi - Non-perturbative...
a second solution: partial brane recombination
4 D7 branes with all the D7' branes
a model without D5-branes
C. Angelantonj
I. Antoniadis (1999)
E. Dudas
A. Sagnotti
G. Pradisi - Non-perturbative...
Decomposition of representations
This suggests that the Higgs mechanism captures
the brane recombination for the massless spectra
First Solution
vev
G. Pradisi - Non-perturbative...
Second Solution
Here the Higgs mechanism is more involved
One needs a multiple step procedure and also the introduction of suitable
Discrete Wilson Lines.
The conjecture is: brane recombination is at work. There should exist a way to realize
the transition in a single step, not captured by the Higgs mechanism
G. Pradisi - Non-perturbative...
Two step procedure
Add Wilson lines to distribute the branes for U(16)a U(12) x U(4) and U(16)b U(4)4
then give vev's to the scalars to break U(4)5 U(4)diag