A Consequence of the Quantum Trace Anomaly in Low Energy Gravity E Mottola Los Alamos National Laboratory preprint to appear April 2016 ID: 548974
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Slide1
Scalar Gravitational WavesA Consequence of the Quantum Trace Anomaly in Low Energy Gravity
E.
Mottola
Los Alamos National Laboratory
pre-print to appear April (2016)
w
.
R.
Vaulin
,
Phys. Rev. D
74, 064004 (2006)
w
.
M.
Giannotti
,
Phys. Rev. D
79, 045014 (2009)
Review
:
Acta
. Phys. Pol. B
41, 2031 (2010)
Slide2
OutlineEffective Field Theory & AnomaliesMassless Scalar Poles in Anomaly AmplitudesEffective Theory of Low Energy Gravity
Role of the
T
race Anomaly
New Scalar Degree of Freedom from the Trace Anomaly
Scalar Gravitational Waves in EFT of Gravity
Conformal Part of Metric becomes Dynamical
Astrophysical Sources
Neutron Star Mergers
Black Hole/
Gravastar
MergersSlide3
Effective Field Theory & Quantum Anomalies EFT = Expansion of Effective Action in Local Invariants
Assumes
Decoupling
of Short (
UV
) from Long Distance (
IR
)
But
Massless
Modes do
not
decouple
Massless
Chiral
, Conformal Symmetries are
Anomalous
Macroscopic
Effects of Short Distance physics
Special
Non-Local
Terms Must be Added to Low Energy EFT
IR
Sensitivity
to
UV
degrees
of
freedomSlide4
Quantum Trace Anomaly & Massless Poles Eg. QED in an External EM Field
A
µ
Triangle One-Loop Amplitude as in Axial U(1) Anomalyabcd (p,q) = (k2 gab - ka k b) (gcd p•q - qc pd) F(k2) + (traceless terms)In the limit of massless fermions, F(k2) has a massless pole:
T
ab
J
c
J
d
p
q
k
=
p
+ q
Corresponding Imag. Part Spectral Fn. has a fnThis is a new massless scalar degree of freedom in the two-particle correlated spin-0 stateSlide5
Massless Anomaly PoleFor p2 = q2 = 0 (both photons on shell) and m
e
= 0
the pole at
k
2 = 0describes a massless e+ e - pair moving at v=c collinearly, w. oppositehelicities in a total spin-0 state (relativistic Cooper pair in QFT vacuum) a massless scalar 0+ state which couples to gravity Effective Massless Scalar Propagator Effective vertex h
(g
-
) FF
Special case of general anomaly form Recovered for finite me > 0 if k2 >> m
e2 Slide6
Scalar Pole in Gravitational Scattering
In
classical GR
only transverse
,
tracefree
polarized waves (spin-2) are emitted/absorbed and propagate between sources T´ and T The scalar parts give only non-progagatingconstrained interaction (like Coulomb field in E&M)
But for
m
e
= 0 there is a scalar pole in the TJJ triangle amplitude coupling to photons
This scalar wave propagates in gravitational scattering between sources T´ and
T
Couples to trace T´
Modifies ϒ-
ray deflection
TTT triangle of massless
photons has this pole Scalar degree of freedom in EFT of GravitySlide7
Constructing the EFT of GravityAssume Equivalence Principle (Symmetry)Metric Order Parameter Field g
ab
Only two strictly
relevant
operators
(R,
) Einstein’s General Relativity is an EFTBut EFT = General Relativity + Quantum Corrections Semi-classical Einstein Eqs. (k << Mpl):Gab+ gab = 8p G TabBut there is also a quantum (trace) anomaly:
Taa
= b C2
+ b' (E
- 3 R ) + b" R + c Fab
FabMassless Poles New IR
relevant operator needed
2
E=RabcdR
abcd - 4R
abRab
+ R2
C2=C
abcdCabcdSlide8Slide9
Effective Action for the Trace Anomaly Non-Local Covariant Form (logarithmic propagator)
Local
Covariant
Form in Terms of New Scalar Field
Dynamical Scalar in Conformal Sector: ‘Conformalon’ Slide10
Stress Tensor of the Scalar ConformalonVariation of the Effective Action with respect to the metric gives stress-energy tensor
Macroscopic
Quantum Effect in
Terms
of
(
Semi-)Classical Scalar Conformalon Field Slide11
IR Relevant Term in the ActionNew conformalon
scalar degree
of
freedom couples to the conformal sector of metric and makes it dynamical
The effective action for the trace anomaly scales
logarithmically with distance and therefore
should be included in the low energy
macroscopic EFT description of gravity—Not given in powers of Local Curvature This is a non-trivial modification of classical General Relativity required by quantum effects in the Std. ModelSlide12
Scalar Gravitational Waves Linearize Vacuum Einstein Eqs.
Linear Metric Decomposition
Usual Einstein Constraints now Dynamical
Solved
by Scalar ‘Breathing’ Mode GW Only half of Solns. Couple to metric Slide13
Localized Sources of Scalar Gravitational Waves Retarded Green’s Fn. Anomaly Scalar
Conformalon
Field
Scalar Metric
Peturbation
in Far (Radiation) Zone
Scalar Energy Flux & Power Radiated for Time Harmonic SourceSlide14
Astrophysical Sources of Scalar Gravitational Waves Sources of φ are the trace anomaly terms
Curvature Invariants are typically very small (Planck suppressed)
But E&M and QCD Gauge Field Anomalies are
much
larger
Axion
-Like Particle Coupling to Electromagnetic Field For a Magnetar B ~ 1015 Gauss Still too small for aLIGOSlide15
QCD Sources of Scalar Gravitational Waves The QCD Trace Anomaly is also a Source for φ
Gluonic
Condensate
much
larger (10 Orders of Magnitude!)
Neutron Star Cores contain Density Dependent Gluon Condensate
In a Neutron Star Merger with another Compact Object this Gluonic Condensate (‘Bag Constant’) is almost certainly disturbed Scalar GW Mode most likely excited in Neutron Star Mergers Condensate also plays role in Gravastar Alternative to BH’s Also possible source in cosmological QCD phase transition Slide16
SummaryEinstein’s classical theory receives Quantum Corrections relevant at macroscopic
Distances
This is a
necessary
quantum modification of classical GR
Scalar ‘
Conformalon
’ degree of freedom in the EFT of Low Energy Gravity predicted by the Conformal/Trace AnomalyEFT of Gravity predicts the existence of scalar GWsMost significant astrophysical source of Conformal Scalar Gravitational Waves are disturbances in the gluonic vacuum energy ‘bag constant’ of dense nuclear matter in Neutron Star Mergers with other compact objectsScalar Gravitational Waves should be looked for by aLIGO and next generation of GW detectors Slide17
Exact Effective Action &Wilson Effective ActionIntegrating out Matter + … Fields in Fixed Gravitational Background gives the Exact Quantum Effective ActionThe possible terms in Sexact
[g
]
can be classified according to their
repsonse
to
local Weyl rescalings g e2 g Sexact[g] = Slocal[g] + Sanom[g] + SWeyl[g] Slocal[g] = (1/16G) d4x g (R - 2 ) + n≥4 MPl4-n S(n)local[g] Ascending series of higher derivative local terms, n>4 irrelevantNon-local but Weyl-invariant (neutral under
rescalings)
SWeyl[g
] = SWeyl[e
2g]
Sanom[g] special non-local terms that scale linearly with , logarithmically with distance, representatives of non-trivial cohomology under
Weyl groupWilson effective action captures all IR physics S
eff[g] = Scl
[g] + Sanom[g
; φ]