an update on brane susy breaking · 2017-06-22 · an update on brane susy breaking augusto...

An Update on Brane SUSY Breaking

Augusto SagnottiScuola Normale Superiore and INFN – Pisa

International School of Subnuclear Physics, 55thCourse Erice- Sicily, June 14-23 2017

C. Angelantonj and AS, “ Open strings,''Phys. Rept. 371 (2002) 1 [hep-th/0204089], and refs therein.

A. Sagnotti - Int. School of Subnuclear Physics 2017

Ten-Dimensional Superstrings

2


Building principles of (closed) string spectra VACUUM ENERGY

• spin-statistics (GSO projections)

• modular invariance(ττ+1 ; τ - 1/τ)

Closed Superstrings

3

(Gliozzi, Scherk, Olive, 1977):


Building principles of (closed) string spectra and the vacuum energy:

• spin-statistics (GSO projections)

• modular invariance

10D Building Blocks: SO(8) level-one characters ( ):

Scalar (Vector)+ ... SpinorL (SpinorR)+ ...

Modular Transformations:

Ten-Dimensional (Closed) Superstrings

4

SUSY:

(Gliozzi, Scherk, Olive, 1977):


• IIA, IIB:

• HE, HO:

• 0A, 0B:

• H16x16:

Ten-Dimensional (Closed) Superstrings

5


An example: IIB IIA (g=(-1)Fright)

• IIA, IIB:

1) Projection:(Untwisted Sector)

S :

2) Modular invariance: T :(Twisted Sector)

• ALTOGETHER :

Orbifolds

6

(Dixon, Harvey, Vafa, Witten, 1985).....(Antoniadis, Bachas, Kounnas, 1987)


Models with OPEN strings DESCEND from closed onesvia orientifold projections MIX L and R string MODES(+ M. Bianchi, G. Pradisi, 1988- ; Y. Stanev, 1994-)

New 2D ingredients:

RR tadpole(s): neutrality conditions

The procedure fills vacua with D-branes and O-planes(Polchinski, 1995)

Open Descendants, or “Orientifolds”[LR]

7

(AS, 1987)


1) Klein amplitude K: “diagonal” torus sectors, differentchoices regulated by “fusion”. Determines the crosscap-crosscap exchange via an S transformation. CONSISTENT?

2) Boundary-boundary exchange from all diagonal torussectors, reflection coefficients determine the CHAN-PATON factors. Annulus amplitude A by an Stransformation.

3) Boundary-crosscap amplitude: reflection coefficients thatare (twice) the “geometric means” of those of the otherexchange amplitudes.

4) Mobius amplitude: follows by a “P transformation” :

RR tadpole(s): neutrality conditions

Open Descendants, or “Orientifolds”

8

O-T<0, Q<0


1) SO(32) type-I (Green and Schwarz, 1984): DESCENDS from IIB. In vacuum BPScombination (O- orientifold (T<0,Q<0) and D-branes (T>0,Q>0)). Massless Weylfermions in the adjoint of SO(32)

10D Tachyon-Free Orientifolds

9

D-branesT>0, Q>0


10D Tachyon-Free Orientifolds

1. U(32) type-0’b:

[NO SUSY, T > 0 ] (AS, 1995)

2. USp(32) type-I: [non-linear SUSY, T > 0 ] (Sugimoto, 1999)

10

O+T>0, Q>0

D-antibranesT>0, Q<0

Only sign of V flipped w.r.t. type-

I SO(32)!


Brane SUSY Breaking (BSB)

11


String Theory : efficiently described around supersymmetric vacua (especially with extended SUSY)

On the other hand, broken supersymmetry vacuum redefinitions:

• Only oriented closed strings from “loop” diagrams (torus and beyond)• Orientifolds distinction between trees and loops is blurred by open-closed duality

• “Brane SUSY Breaking”: in vacuum non-BPS combinations of BPS branes and orientifolds. NO TACHYONS!(Sugimoto; Antoniadis, Dudas, AS; Angelantonj, Aldazabal and Uranga, 1999)

• Runaway exponential potential for dilaton (~ 𝑒𝑒−𝜑𝜑 in string frame, or ~ 𝑒𝑒32𝜑𝜑 in 10D in Einstein frame)

• [ Torus (genus-one) correction in 10D closed-string modes: ~1 in string frame, or ~ 𝑒𝑒52𝜑𝜑 in Einstein frame ]

In Field Theory can shift fields In String Theory must start around “wrong vacua”

The Problem

12

Brane SUSY Breaking (BSB) (Sugimoto, 1999)(Antoniadis, Dudas, AS, 1999)(Angelantonj, 1999)(Aldazabal, Uranga, 1999)

BSB: Tension unbalance “critical” exponential potential

Tree – level

SUSY broken at stringscale in open sector, exact in closed sector

Stable vacuum (classically)

Goldstino in open sector


[ Same exponential (from D – anti D): KKLT uplift (2003) ]


BSB: a 9D Vacuum(Dudas, and Mourad, 2000, 2001)

1. 9D solution that (in string frame) describes an S1/Z2 (interval) compactification.

Finite 9D Planck mass and gauge coupling, but singularities at the ends

[ similar, albeit more complicated looking, results also for the heterotic SO(16) x SO(16) ]

2. HOWEVER: two kinds of problems with this solution:

a) string loop corrections: determined by the second equation, grow out of control for y ∞;

b) curvature corrections: large near y=0.

14


BSB: Inflation after a bounce?(Dudas, Kitazawa, AS, 2010)

1. “Critical” tadpole exponent: precisely at the onset of the “climbing phenomenon”.

2. Scalar bound to emerge from initial singularity “climbing up” potentials that

correct BSB by softer terms. Now bounded string loop corrections.

3. Slow-roll after bounce and deceleration: last stages were imprinted in CMB ?

low-l lack of power [& low-l enhancement of tensor-to-scalar ratio r].

(Lucchin, Matarrese, 1985)(Halliwell , 1987)…………(Dudas, Mourad, 2000)(Russo, 2004)(Dudas, Kitazawa, AS, 2010)…………

15


(Pre-)Inflation with a Bounce (Dudas, Kitazawa, AS, 2010)

1) LOW l CMB: low-l lack of power from a decelerating inflaton ? (possibly low-l increase of tensor-to-scalar ratio)

IF WE ACCESS, via the CMB, to the onset of slow roll;

2) PLANCK 2015 (high latitudes):16

(Gruppuso, Mandolesi, Natoli, Kitazawa, AS, 2015)


AdS Vacua and Branes

from

Dilaton Tadpoles and Fluxes

17


Low-Energy Lagrangians

Three 10D tachyon-free string models:

In string frame (T Λ for heterotic):

In Einstein frame (T Λ for heterotic):

Here:

Orientifolds:

Heterotic:

18

- Heterotic SO(16) x SO(16) [NO SUSY]- 0B’ U(32) ORIENTIFOLD [ NO SUSY]

- BSB Usp(32) ORIENTIFOLD [NON-LINEAR SUSY]

(Mourad, AS, 2016)


Brane Profiles

1. The starting point is a class of metrics of the type (whose structure is familiar from the SUSY case):

2. CFT analysis of (charged and uncharged) brane configurations for this type of orientifold systems.

(Dudas, Mourad, AS, 2001)

How will the CFT analysis, which is set up around the flat space empty vacuum, and thus ignoring

the dilaton tadpole, connect to the actual deformed backgrounds?

19


Radial Dynamical SystemSecond-order equations: ( )

First-order constraint:

20


Example: Supersymmetric Branes

Gauge choice:(k=0,k’=1)

A ~ B ~ φ :

If βE ≠ 0 :

21


Non-Singular Vacuum Configurations

1) The class of metrics:

2) Constant dilaton profiles : aim at “fixing” the dilaton, despite the runaway potentials

3) Vacuum configurations for :

22


Orientifold Vacuum ConfigurationsIn this fashion the field equations reduce to

(∗): Dilaton eq: strong constraint due to positivity of l.h.s. (βE < 0 for orientifolds & T>0, NEED H3 fluxes)

First two eqs: determine k’=1 (internal sphere), and its radius R=eC and φ in terms of h

Third eq: determines for k=0 A ~r, and thus AdS in Poincaré coordinates (or in other slicings for k ≠ 0)

23

Let us take a closer look at the last equation:

It is solved by:

These metrics emerge from three different slicing of the same AdS space, for which

1. K = 1 slicing:

2. K=-1 slicing:

3. K=0 slicing:


AdS Slicings

24

This solution:

exists only for T ≠ 0

contains a perturbative corner (large R, small gs)

[reasons to expect that one is solving the complete string equations]

accommodates a residual unbroken gauge group (Usp(32) or U(32))

We have now some indications that it is perturbatively stable

(I. Basile, J. Mourad, AS, ongoing)


AdS3 x S7 Orientifold Vacua ( )

25


Heterotic Vacuum ConfigurationsIn this fashion the field equations reduce to

(∗): Dilaton eq: Λ > 0 and we can allow unbounded H7 fluxes (they have βE < 0).

First two eqs: determine again k’=1 (internal sphere), and (implicitly) its radius R=eC and φ in terms of h

Third eq: determines again for k=0 A ~r, and thus AdS in Poincaré coordinates (or in other slicings for k ≠ 0)

26


AdS7 x S3 Heterotic Vacua ( )

27

This solution:

exists only for Λ ≠ 0

contains a perturbative corner (large R, small gs)

[reasons to expect that one is solving the complete string equations]

accommodates a residual unbroken SO(16) x SO(16) gauge group

We have now some indications that it is perturbatively stable

(I. Basile, J. Mourad, AS, ongoing)

• SUSY BREAKING: NOT ONLY technically difficult in String Theory. IT ALSO raises conceptual issues.

• Vacuum is redefined can start around a wrong vacuum and try to approach a proper description viasuccessive corrections. FIRST STEPS via the low-energy effective field theory:

- ∃ (Homogeneous) vacua of AdS x S type, with regions of parameters where the two couplingsthat determine the corrections are small.

- AdS3xS7 ORIENTIFOLD and AdS7xS3 HETEROTIC solutions: supported by H3,7 fluxes

- we have some indications that they are perturbatively stable. Non perturbatively ?

Can one do better, exploring richer 10 4 compactifications, and also back-reaction on branes ? Let us see...


Summary and Outlook

28

Thank You


an update on brane susy breaking · 2017-06-22 · an update on brane susy breaking augusto...

Documents