Miami 2012

Tirtho Biswas

Stringy Nonlocal Theories

My Collaborators• N. Barnaby (University of Minnesota)• R. Brandenberger (McGill)• J. Cembranos (Madrid)• J. Cline (McGill)• M. Grisaru (McGill)• J. Kapusta (U of M)• T. Koivisto (Utrecht)• A. Kosheylev (Brussels)• A. Mazumdar (Lancaster)• A. Reddy (U of M)• W. Siegel (Stony Brook)• S. Vernov (Moscow)

• TB, J. Cembranos and J. Kapusta,  PRL 104, 021601 (2010)  [arXiv:0910.2274 [hep-th]]

• TB, E. Gerwick, T. Koivisto and A. Mazumdar,  PRL 108, 031101 (2012)  [arXiv:1110.5249 [gr-qc]]

OutlineNonlocal Scalar Field Theory

Stringy Motivations Ghostfree higher derivative theories Finite Loops & some results

Nonlocal Gravity The problem of Ghosts Nonsingular Black Holes? Nonsingular Cosmology?

String Field Theory Tachyons [Witten, Kostelecky &

Samuel, Sen]

Mass square has the wrong sign

p-adic string theory [Volovich, Brekke, Freund, Olson, Witten,

Frampton]

An inifinte series of higher derivative kinetic operators, mildly nonlocal

)()(2

11 2

2

222

Vemxdg

S MD

o

Open string coupling string tension

Nonlocal Actions in String Theory

1

2

2

2 1

1exp

2

1 pD

p

Ds

pMxd

g

mS

Interesting PropertiesGhostfree

But SFT/padic type theories have no extra states!

Quantum loops are finite UV under better control, like usual HD theories

Linear Regge Trajectories [TB, Grisaru & Siegel]

Thermal duality [TB, Cembranos & Kapusta, 2010 PRL]

Can there be any phenomenological implications for LHC? [Moffat et al]

2222222

222222

11~

)(

1~)(

0)()(2

1~

mppmppp

mmxdS D

)(2

11

T

mZTZ s

22

222 )exp()(

mp

Mpp

Applications

Insights into string theory Brane Physics & Tachyon condensation [Zwiebach & Moeller;

Forini, Gambini & Nardelli; Colleti, Sigalov & Taylor; Calcagni…]

Hagedorn physics [Blum; TB, Cembranos & Kapusta]

Spectrum [TB, Grisaru & Siegel, Minahan]

Applications to Cosmology Novel kinetic energy dominated non-slow-roll

inflationary mechanisms [TB, Barnaby & Cline; Lidsey…]

Large nongaussianities [Barnaby & Cline]

Dark Energy [Arefeva, Joukovskaya, Dragovich, ...]

Applications to Particle Physics [Moffat et.al.]

Nonlocal Gravity

Can Nonlocal higher derivative terms be free from ghosts?

Can they address the singularity problems in GR ?

What about quantum loops? Stelle demonstrated 4th order gravity to be renormalizable

(1977), but it has ghosts

Ghosts

From Scalars to Gravity The metric has 6 degrees (graviton, vector, and

two scalars)

Gauge symmetry is subtle, some ghosts are allowed

Several Classical (time dependent) backgrounds.

Linearized GravityFree from ghosts in Minkowski vacuum Only interested in quadratic action [with Mazumdar, Koivisto,

Gerwick, 2012 PRL]

Only 6 linearly independent combinations using BI

Covariant derivatives must be Minkowski, most general form

''''''''4 ˆ

)(~

RORRgxdS

hORhg

...)()()( 23

22

21

4

RFRRFRRRFRgxdS

hf

hhhd

hhchbhhahxdS

2

222

22224

)()(

2

1

)()()(2

1

Covariant to Minkowski

We noticed rather curious relations

They in fact follow from Bianchi identity! By inverting Field equations we obtain the

propagators Decouple the different multiplets using projection

operators: [van Nieuwenhuizen]

Precisely because of the above relations, the dangerous w-scalar ghost and the Vector ghost vanishes

)(2)(2

11)( 32 xxFxxFxa

0

0

0

fac

dc

ba

0012 ,,, ws PPPP

General Covariance dictates the propagator is of the form

At low energies, p 0, we automatically recover GR In GR a = c = 1, scalar ghost cancels the longitudinal

mode a has to be an entire function, otherwise Weyl ghosts a-3c can have a single zero -> f(R)/Brans-Dicke theory Exponential non-local Gravity,

2

0

2

2

222

0

22

22

2

1

)](3)([)()(

p

P

p

P

ppcpa

P

ppa

Pp sGRs

2

2exp

Mca

2

2

2

0

2

22 exp

2

1)(

M

p

p

P

p

Pp s

Newtonian Potentials

Large r, reproduces gravity; small r, asymptotic freedom

No small mass black holes, no horizon and no singularity!

Gravity Waves Similar arguments imply nonsingular Green’s

functions for quadrupole moments

)()21()21( 00222 rmanddxdtds

r

Mr

p

eepdrr

ripMp )(erf~~)()(

2

./3

22

M

Mm p

2

Exact SolutionsBouncing Solutions deSitter completions, a(t) ~ cosh(Mt)

Stable attractors, but there are singular attractors.

Can provide a geodesically complete models of inflation.

Perturbations can be studied numerically and analytically, reproduces GR at late times… can provide geodesic completion to inflation

RRFRgxdS )( 21

4

Conclusions

Nonlocal gravity is a promising direction in QG

It can probably solve the classical singularities

How to constrain higher curvatures? New symmetries Look at ghost constraints on (A)dS – relevant for

DE Can we implement Stelle’s methods?

Emergent Cosmology Space-time begins with pure vacuum

You cannot find a consistent solution for GR There must be a scalar degree of freedom

0 ttandg

1)(1)( tt taeta

0)(3)( 22 ca

mandpawithmpac ~)exp()/1( 222

t’ Hooft dual to string theory Polyakov action:

Strings on Random lattice [Douglas,Shenker]

Dual Field theory action

Motivation Standard Models of Particle Physics &

Cosmology have been remarkably successful

Too successful, no experimental puzzles Hints at new meV physics (Dark energy &

Neutrinos) Fall back on theoretical prejudices

Hierarchy problem, Unification - GUT, SUSY, String Theory

Nonsingularity – can we use this to guide us?