Higher Derivative Scalars in - PowerPoint Presentation

Slide1

Higher Derivative Scalars in Supergravity

Jean-Luc Lehners

Max Planck Institute for Gravitational Physics

Albert Einstein

Institute

Based on work with Michael

Köhn

and Burt

OvrutSlide2

Motivation

Assume

N

=1

s

upersymmetry

is a good symmetry at an early phase

Aim to construct a corresponding effective theory for scalar fields

Can be applied to inflation,

ekpyrosis

, ...

Extension of 1012.3748,1103.0003 (

Khoury

, JLL,

Ovrut

)

1109.0293 (Baumann, Green)Slide3

General Features

Multiple scalars, as a chiral

multiplet

contains

two

real scalarsNatural setting for some curvaton models of inflation and entropic mechanism in ekpyrosisSusy constrains scalar field actions e.g. consequences for non-gaussianity New effects from eliminating auxiliary fieldsSlide4

Construction

Chiral

multiplet

Spin ½ Auxiliary field

Superspace

Complex scalar

Kähler

potential

e.g.Slide5

First concentrate on where

Rewrite

Strategy: construct first

everything else will follow easily!

For need two more fields and two more derivatives/four superspace derivatives sinceSlide6

Only two “clean” possibilities (want

not )

chiral integral

To go to

supergravity

integrate over curved superspace and use curved chiral projector contains Ricci scalar andSlide7

Includes

Second scalar

not of P(X) form

Interesting –

modifies gravity sector too!

More worrying –

Auxiliary field not auxiliary anymore!Slide8

Focus on

w

hich equals

Scalar action

No new coupling to Ricci scalar

- No kinetic term for auxiliary field F- All terms involving auxiliary fields of supergravity multiplet

also involve fermionsSlide9

P(X) in supergravity

All lower components of

contain fermions!

Hence now easy to construct

sugra

extension of any term that contains as a factor:To get usebut now withIn this way one can build up P(

X,

f

) as a Taylor series Slide10

Ghost Condensate

When the kinetic function P(X) has

a minimum, develop a time-

dependent

vev

for f: Typical action: Minimum corresponds to

dS

space

Perturbations around

minimum allow

stable violations of NEC for short

periods of time

Can be used to model dark energy or non-singular bounces

X

P(X)Slide11

Ghost condensate in supergravity

Omitting the second real scalar, up to quadratic order in fermions action becomes:

Vacuum breaks Lorentz invariance, manifested by wrong sign spatial gradient term for

goldstino

Mixed mass term for

gravitino-goldstino

super-Higgs?Slide12

Super-Higgs

Susy

transformation

Usual F-term breaking: DW≠0, A=0

Gravitino eats goldstino and becomes massiveHere W=0, but √2A =

f

= t, hence

goldstino

also shifts by a constant

:However, there is no superpotential and hence no mass term for the

gravitino - so what happens?Slide13

Redefine gravitino

to get rid of mixed mass term:

Action

Gravitino

remains massless!

Goldstino remains present, otherwise degrees of freedom would be lostGoldstino kinetic term has a different normalization This is the indication that

susy

is really brokenSlide14

Eliminating the auxiliary field F

Add only X - equation of motion for F is

Equation for F is

cubic

raises interesting question as to how one defines the quantum theory there are now new solutions that correspond to new branches of the theory

2

c

oefficient of X

2Slide15

Perturbing around usual solution

X term contributes

For small c2, solve

Hence a new, higher-derivative

kinetic

term modifies the potential

2

Corrections to

kinetic term

Corrections to

t

he potentialSlide16

Example: W=A

Leads to a potential

o

f the form

Corrections go as

For c2>0 turns a valleyinto a mexican hat!Slide17

New Branch of Supergravity

Turn

superpotential

off: W=0

Then

eq for F readsSolved not only by F=0, but also bySlide18

Without fermions, whole action becomes

-

Ordinary

kinetic term has vanished

A potential (depending on the

Kähler potential) has appearedScale of potential:

Mass of

f

Not continuously

connected to

o

rdinary branchSlide19

Dynamics: for

t

he

a

ction becomes

In a θ~ x background, need c2>0 so thatρisn’t a ghostThen the potential is positive, which is unusual for supergravity

(the size of the potential is limited by the

vev

of

θ)Slide20

Summary

B

reak

susy

with ghost condensate

Unusual way of breaking supersymmetry: the gravitino remains massless, and a kinetic term for the “goldstino” remains presentAuxiliary field F leads to new effectsSolutions that are close to the standard solution for F imply that the new higher-derivative kinetic terms correct both the kinetic terms and the potential

New solutions for F lead to entirely new branches of the theory. Their physical significance is not clear yet!