Higher Derivative Scalars in Supergravity Jean-Luc Lehners Max Planck Institute for Gravitational...
-
Upload
suzanna-robinson -
Category
Documents
-
view
216 -
download
0
Transcript of Higher Derivative Scalars in Supergravity Jean-Luc Lehners Max Planck Institute for Gravitational...
Higher Derivative Scalars in Supergravity
Jean-Luc LehnersMax Planck Institute for Gravitational Physics
Albert Einstein Institute
Based on work with Michael Köhn and Burt Ovrut
MotivationAssume N =1 supersymmetry is a good symmetry at an early phaseAim to construct a corresponding effective theory for scalar fieldsCan be applied to inflation, ekpyrosis, ...
Extension of 1012.3748,1103.0003 (Khoury, JLL, Ovrut) 1109.0293 (Baumann, Green)
General FeaturesMultiple 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 fields
ConstructionChiral multiplet
Spin ½ Auxiliary field
Superspace
Complex scalar
Kähler potential
e.g.
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 since
Only two “clean” possibilities (want not )
chiral integralTo go to supergravity integrate over curved superspace and use curved chiral projector
contains Ricci scalar
and
Includes
Second scalar not of P(X) form
Interesting – modifies gravity sector too!
More worrying – Auxiliary field not auxiliary anymore!
Focus on
which 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 fermions
P(X) in supergravityAll lower components of contain fermions!
Hence now easy to construct sugra extension of any term that contains as a factor:To get use
but now with
In this way one can build up P(X,f) as a Taylor series
Ghost CondensateWhen the kinetic function P(X) has a minimum, develop a time-dependent vev for : f
Typical action:
Minimum corresponds to dS spacePerturbations 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)
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 goldstinoMixed mass term for gravitino-goldstino super-Higgs?
Super-HiggsSusy transformation
Usual F-term breaking: DW≠0, A=0 Gravitino eats goldstino and becomes massive
Here 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?
Redefine gravitino to get rid of mixed mass term:
Action
- Gravitino remains massless!- Goldstino remains present, otherwise degrees of
freedom would be lost- Goldstino kinetic term has a different
normalization This is the indication that susy is really broken
Eliminating the auxiliary field F
Add only X - equation of motion for F is
Equation for F is cubicraises interesting question as to how one
defines the quantum theorythere are now new solutions that correspond
to new branches of the theory
2
coefficient of X2
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
the potential
Example: W=A
Leads to a potentialof the form
Corrections go as
For c2>0 turns a valleyinto a mexican hat!
New Branch of Supergravity
Turn superpotential off: W=0
Then eq for F reads
Solved not only by F=0, but also by
Without fermions, whole action becomes
- Ordinary kinetic term has vanished- A potential (depending on the Kähler
potential) has appeared
Scale of potential: Mass of f
Not continuously connected to ordinary branch
Dynamics: for
the action 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)
Summary• Break susy with ghost condensate
Unusual way of breaking supersymmetry: the gravitino remains massless, and a kinetic term for the “goldstino” remains present
• Auxiliary field F leads to new effectso Solutions 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
o New solutions for F lead to entirely new branches of the theory. Their physical significance is not clear yet!