non-perturbative transitions among intersecting...

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

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

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

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

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)

Reps and Multiplicities of charged hypermultiplets in T4/Z2

Stack a The intersection numbers determine the multiplicities

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)

(Partial) recombination to a single additional factorizable stack

A first solution: complete brane recombination

R. Blumenhagen

V. Braun

B. Koers (2002)

D. Luest

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

Decomposition of representations

This suggests that the Higgs mechanism captures

the brane recombination for the massless spectra

First Solution

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

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

BSB orientifold vacua

2-cycles wrapped by O7-planes

real charges

Invariant cycles where

s revert the twisted sectors projection

Exotic O-plane: T>0 , Q>0 (It requires anti-D-branes…)

I. Antoniadis

E. Dudas (1999)

A. Sagnotti

fractional branes now combine into physical brane charged wrt twisted forms

• the action of orbifold on the Chan Paton charges affects the multiplicities

• D-branes wrapping the same O-plane cycles give rise to O and USp groups

• in d=6 supersymmetry is necessarily broken (in the open sector)

the invariant cycles have now components also along the exceptional cycles

Additional constraints are required for Brane Recombination

In order to be a consistent cycles:

• the twisted charges must combine to be non-zero on four collapsed cycles

• the twisted and the untwisted cycles must be compatible

This condition supplements the RR charge conservation in brane

recombination

the SO(16)2 x Usp(16)2 model8 copies of four stack of (orthogonal) physical branes:

a first solution: complete brane recombination

The resulting cycles seems to be of a "bulk" type. The correct interpretation is as a pair

of fractional cycles providing a U(8) x U(8) gauge group

One cannot combine a pair of them. At least three different stacks must participate

(unless one moves them in the bulk, see later)

Anti-D-branes

I. Antoniadis

E. Dudas (1999)

A. Sagnotti

a second solution: partial brane recombination

A choice consistent with all the constraints is as follows

The final configuration is

(a model without anti-D5-branes)

C. Angelantonj

I. Antoniadis (1999)

E. Dudas

A. Sagnotti

The gauge group is SO(16) x SO(8) x U(4)

decomposition of representations

the first solution

Vector

Multiplet

Too many states stay massless

The other fields acquire a mass thanks to couplings

Fermions :

Bosons:

Recombination in the BulkIn the presence of coincident images, one can also move the branes in the bulk

Do Recombination and Displacement Commute?

1. Recombination of the fractional branes

superHiggs

2. Recombination of the bulk branes

No way to get 8 L fermions in 28

The 1-loop Effective Potential

One-Loop effective potential (free energy) for vev's of positions and WL's

Better the transverse channel

• a divergent tadpole contribution

• divergent when branes are on top of the O-planes

For only R1 much bigger than alpha' one gets

One should evaluate

The effective action

string frame

Einstein frame

expanding

Is it meaningful?

• massive state contributions are suppressed

• the tadpole is subtle but we know from similar calculation that the

resummation produces no corrections to the gaugino mass E. Dudas

M. Nicolosi

G.P. (2004)

A. Sagnotti

Classical Solutions

and Brane Transmutation

Now we go back to the T-dual D9-D5 system

1. The two-dimensional case (not really D5-D9)

We want to describe solutions in which the

D5 brane dissolves into the D9 brane

The vev of the scalars can be modeled by

a Fayet-Iliopoulos term in the effective action

It corresponds to a d=6 SYM compactified on a two-torus

N. Arkani-Hamed

T. Gregoire (2001)

J. Wacker

Localized source

The solution generates, as expected, a constant flux

Ansatz

Zero-mode of the Laplacian

Choosing

2. The four-dimensional case (D5-D9)

Ansatz

Solution

3. A closer look

violates anti-self-duality

locally

A constant magnetic field

4. Can non-linear corrections soften the singularity?

Using the Ansatz in the Born-Infeld eom

and looking for perturbative corrections

Singularity not affected. Large distance ok. [see ]

M. Billo'

M. Frau

A. Lerda (2005)

S. Sciuto

G. Vallone

4. Can higher derivative terms soften the singularity?

Hopefully yes! however

The abelian part of the SU(2) Instanton solution

cannot be the constant magnetic field !

Four dimensional examples

Homology similar to the 6d case

bulk 3-cycles

exceptional 3-cycles

generic 3-cycle

O6-planes

discrete torsion

Our choice

Can we connect susy and non-susy models?

1. a BSB model with orthogonal 6-branes/antibranes:

gauge group

2. a susy model with rotated 6-branes/antibranes:

gauge group

3. another susy model with rotated 6-branes/antibranes

gauge group

C. Angelantonj

I. Antoniadis

D'Appollonio (2000)

E. Dudas

A. Sagnotti

E. Dudas

C. Timirgaziu (2005)

P. Camara

C. Condeescu (2010)

E. Dudas

M. Lennek

• 1. 2. OK

• 1. 3. Not allowed. There are not enough D6 in the h-direction.

One possibility is to add brane-antibrane pairs.

• 2. 3. ???

Higgsing?

• alpha' corrections needed: BI?

• What are these bound states in the LEEA?

Conclusions

Brane Recombination is a mechanism that connects (non-perturbatively)

orientifold vacua differing for the brane configuration. It works also for

vacua that are non supersymmetric but classically stable (BSB).

At the level of effective action, in the simplest supersymmetric cases, it is

captured by an Higgs mechanism. In the non-susy cases the low energy

description is subtle and requires additional ingredients.

It is T dual to inverse "small-instanton" transition (brane transmutation)

but the magnetic field flux is due to finite volume effects.

It connects non-perturbatively non-susy to susy orientifold vacua.

Thank you

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