On the running of the coupling constants in gravity 1

MOHAMED ANBER

UNIVERSITY OF TORONTO LOOPS 2013

M.A., J. Donoghue, M. El-Houssiney; Arxiv: 1101.3229 M.A., J. Donoghue; Arxiv: 1111.2875

M. Anber, Loops 2013

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Outline 2

 Renormalization group in perturbatively renormalized field

theory  Effective field theories: Gravity as an effective field theory,

renormalization and standard results  Running couplings in the presence of gravity

 Running of the gravitational coupling constant

M. Anber, Loops 2013

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RG in field theory, review 3

 The perturbation expansion parameter is dimensionless

parameter  Perturbatively renormalized theory: only a finite number of

counter terms for all loop orders  E.g.  

1   2   4 2

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RG in field theory, review 4

 Perturbatively renormalized theory: 3i2  iM  i  32 2

i2 2     log 4     24 2  

renormalize at

 4 theory

 s  t    u  log 2   log 2   log 2         

s  t  u  4M 2 / 3

3i2  i ( M )  i  32 2

2  4M 2  2  3i    log 4     24 2 log 3 2     

32     16 2

Universal!

 i2 E    s   t   u   iM  i E   log 2   log 2   log 2   i  2  24    2 E   2E   2E   M. Anber, Loops 2013

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RG in field theory, review 5

 The same result if we perform on-shell renormalization

s  2E , t  u   E , log s   log s  i 2

2

 Beta-function is universal, it sums the logs and it is robust

against symmetry crossing problem  Non-analytic pieces:

effects

M. Anber, Loops 2013

log q^2 are long range quantum

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Effective field theory 6

 We do not have a dimensionless expansion parameter,

instead we expand in powers of

E 

 Effective field theories are not perturbatively renormalized:

you need an infinite number of counter terms

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Gravity as an effective field theory 7

 Einstein gravity is an effective field theory:

   We take

2

2

R

,  2  32G

E Mp

as our expansion parameter  Gravity is not perturbatively renormalized: loop corrections demand an infinite number of counter terms

 

2

2

R  c1R 2  c2 R  R    ...

 Pure gravity is finite to one-loop: since

M. Anber, Loops 2013

R   0

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Standard results in quantum gravity 8

 Quantum corrections to lower order operators are absorbed

in higher order operators ‘t Hooft and Veltman dim reg

Graviton propagator

scalar

c1R 2  c2 R  R  

 Non-local remnants will have effect on the low energy

physics:

log( q 2 ),  q^2 Quantum piece

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Classical piece 7/26/2013

Standard results in quantum gravity 9

 Classical and quantum corrections to Newton’s potential

GmM c1 (m  M ) G V [1   c2 2 3 ] 2 r rc r c

Quantum correction Classical, post Newtonian

 This is a quantum

gravity prediction! Donoghue 94 Donoghue, Holstein, Bjerrum-Bohr 2002 M. Anber, Loops 2013

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Running couplings in gravity 10

 Does the inclusion of gravity improves the UV behavior of

the coupling constant of non-asymptotically free theory, like QED or Yukawa? Asymptotic safety people, Robinson and Wilczek 2006  Since this work, many other works appeared : run or not to

run? Improve or not?  Does the running make sense in the presence of gravity?

M. Anber, Loops 2013

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Running couplings in gravity 11

 Yukawa + gravity

g

M.A., J. Donoghue, M. ElHoussiney; Arxiv: 1101.3229

  1, time - like   -1, space - like

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Running couplings in gravity 12

 Trying to define a running coupling:

Non-universal Symmetry crossing problem!

 The running of the coupling does not make sense!

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Running of the gravitational coupling 13

 Let us see if we can define a running of the gravitational

coupling



M.A., J. Donoghue; Arxiv: 1111.2875

 1) vacuum polarization

For space like: increase in G For time like: decrease in G In Euclidean: increase in G M. Anber, Loops 2013

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Running of the gravitational coupling 14

 2) scattering of gravitons in pure gravity Dunbar and Norridge

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Running of the gravitational coupling 15

Donoghue and Torma

G increases with increasing E Non-universality! M. Anber, Loops 2013

G increases with increasing E But different coefficient 7/26/2013

Running of the gravitational coupling 16

 Scattering of massless scalars through gravitons Dunbar and Norridge

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Running of the gravitational coupling 17

G decreases with increasing E! Opposite to the pure gravity case!

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Running of the gravitational coupling 18

 Different scalars (only t-channel)

G decreases with increasing E! Symmetry crossing

G increases with increasing E! Crossing symmetry problem! M. Anber, Loops 2013

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Conclusion 19

No universal and useful definition of running constants in gravity, at least in the perturbative region!  Raises questions about nonperturbative attempts in gravity: asymptotic safety program 

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