Viability of quantum-gravity induced ultraviolet completions for matter Aaron Held based on work with Astrid Eichhorn 1705.02342 Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
Standard Model Buttazzo et.Al. ‘13, 1307.3536 1
Landau poles Standard Model Standard Model 18 free parameters Buttazzo et.Al. ‘13, 1307.3536 1
s c Standard Model Standard Model i s y h p e l a 18 free c parameters s k c n a l P Buttazzo et.Al. ‘13, 1307.3536 1
Question: Can quantum gravity provide a UV completion for the Standard Model? 2
What I have to tell ... (1) concepts of asymptotic safety (& the FRG) (2) global symmetries and the fixed-point structure (3) good approximations: spin-2 rules (4) observational constraints on gravity couplings (a) weak-gravity bound (b) linking electroweak- (IR) and Planck-scale physics 3
Asymptotic safety & the FRG 4
Asymptotic freedom Scale invariance at a Gaussian fixed point ( GFP ) ensures a free (perturbatively renormalizable) UV theory g g UV = 0 UV 5
Asymptotic Asymptotic freedom safety Scale invariance at a Gaussian fixed Scale invariance at a non-Gaussian fixed point ( NGFP ) ensures a safe (non- point ( GFP ) ensures a free (perturbatively renormalizable) UV theory perturbatively renormalizable) UV theory g g g UV = const g UV = 0 UV UV 5
Asymptotic safety conjecture Weinberg ‘80 ● existence of a UV fixed point for metric field theory ( fundamental theory ) ● finite number of UV- attractive directions ( predictivity ) ● UV-attractive (relevant) direction: needs to be fixed by experiment ● UV-repulsive (irrelevant) direction: prediction of asymptotic safety 6
Asymptotic safety conjecture Weinberg ‘76 Flows towards IR 7
Asymptotic safety conjecture Weinberg ‘76 UV-attractive (relevant) Flows towards IR 7
Asymptotic safety conjecture Weinberg ‘76 UV-repulsive (irrelevant) UV-attractive (relevant) Flows towards IR 7
Asymptotic safety conjecture Weinberg ‘76 ● UV-attractive (relevant): consistent with any IR value 8
Asymptotic safety conjecture Weinberg ‘76 ● UV-attractive (relevant): ● UV-repulsive (irrelevant): consistent with any IR value predictive 8
microscopic action functional RG prediction of asymptotic safety quantum effective action RG-scale dependent effective action 9
microscopic action functional RG prediction of asymptotic safety quantum effective action RG-scale dependent effective action flow equation RG-scale dependent effective action Wetterich ‘93 9
microscopic action functional RG prediction of asymptotic safety quantum effective action super trace Full regularized (incl. loop propagator momentum) RG-scale dependent effective action Wetterich ‘93 9
microscopic action functional RG prediction of asymptotic safety quantum effective action super trace Full regularized (incl. loop propagator momentum) Gies ‘06, regulator 0611146 insertions RG-scale dependent effective action Wetterich ‘93 9
microscopic action functional RG prediction of asymptotic safety quantum effective action super trace Full regularized (incl. loop propagator momentum) Gies ‘06, regulator 0611146 insertions RG-scale dependent effective action Wetterich ‘93 manifestly 1-loop 9
microscopic action functional RG prediction of asymptotic safety quantum effective action super trace Full regularized (incl. loop propagator momentum) Gies ‘06, regulator 0611146 insertions RG-scale dependent effective action Wetterich ‘93 manifestly 1-loop scalar fluctuating metric fermion 9
RG-flows: truncation and regulator dependence ● Regulators chosen to maintain UV/IR limits ● Truncations also alter fixed point action ➔ choice of truncation Theory space is crucial Gies ‘06, 0611146 10
Global symmetries at the UV FP Maximally-symmetric asymptotic safety 11
Global symmetries at the UV FP 12
Global symmetries at the UV FP 12
Global symmetries at the UV FP 13
Global symmetries at the UV FP 13
Global symmetries at the UV FP scalar Z 2 symmetry scalar shift symmetry chiral U(1) symmetry U(1) phase symmetry combined discrete chiral symmetry finally interested in 14
How to set up truncations spin-2 rules 15
Spin-2 rules 16
Spin-2 rules Newton coupling The traceless-transverse mode dominates (confirmed in all results) cosmological constant higher curvature Scalar curvature couplings are sub-leading 16
Suppression of matter-mediated effects direct gravity contributions matter-mediated . . . 17
Suppression of matter-mediated effects direct gravity contributions matter-mediated including 4-fermion-mediated full result including trace mode spin-2 mode only 17
(4) Observational constraints (a) Weak-Gravity Bound 18
Weak-Gravity Bound gravitational ~ g n+m induction ➢ gravity induces all matter interactions sharing the global symmetries of the matter kinetic terms 19
Weak-Gravity Bound gravitational ~ g n+m induction ➢ gravity induces all matter interactions sharing the global symmetries of the matter kinetic terms ➢ at lowest order quartic couplings ➢ Lowest momentum order ~ g 2 ➢ same for gauge fields Christiansen & Eichhorn, 2017 19
Weak-Gravity Bound canonical pure dimension matter vanishing fixed-point value at possible 20
Weak-Gravity Bound canonical pure induced mixed dimension matter 20
Weak-Gravity Bound canonical pure induced mixed dimension matter g = 6 g = 3 g = 0 Eichhorn, Held, Pawlowski ‘16, 1604.02041 20
Weak-Gravity Bound canonical pure induced mixed dimension matter ● Weak gravity bound: g = 6 ● Too strong gravity leads to an unstable g = 3 matter sector ● these bounds occur for all matter types g = 0 Eichhorn, Held, Pawlowski ‘16, 1604.02041 20
Weak-Gravity Bound Newton coupling The traceless-transverse mode dominates (confirmed in all results) cosmological constant higher curvature 21
Weak-Gravity Bound Newton coupling The traceless-transverse mode dominates (confirmed in all results) cosmological constant higher curvature Eichhorn & Held ‘17, 1705.02342 21
Weak-Gravity Bound Newton coupling The traceless-transverse mode dominates (confirmed in all results) cosmological constant higher curvature similar bound arises in a U(1) gauge theory Christiansen & Eichhorn, 2017, 1702.07724 21
Weak-Gravity Bound Newton coupling The traceless-transverse mode dominates (confirmed in all results) cosmological constant higher curvature Eichhorn & Held ‘17, 1705.02342 21
(4) Observational constraints (b) Linking electroweak- (IR) and Planck-scale physics 22
Linking electroweak- (IR) and Planck-scale physics 23 Buttazzo et.Al. ‘13, 1307.3536
Linking electroweak- (IR) and Planck-scale physics all SM couplings this talk ● are marginal ● do not share global kinetic Christiansen & Eichhorn ‘17, 1702.07724 symmetries Folkerts, Litim, Pawlowski ‘11, 1101.5552 Harst & Reuter ‘10, 1101.6007 ● Gravity acts as anomalous Shaposhnikov & Wetterich ‘10, 0912.0208 dimension 23 Buttazzo et.Al. ‘13, 1307.3536
Linking electroweak- (IR) and Planck-scale physics all SM couplings ● are marginal ● do not share global kinetic symmetries ● Gravity acts as anomalous dimension 23
Linking electroweak- (IR) and Planck-scale physics all SM couplings ● are marginal ● do not share global kinetic symmetries ● Gravity acts as anomalous dimension # TT > 0 SM . . . # TT < 0 Eichhorn & Held ‘17, 1705.02342 23
Linking electroweak- (IR) and Planck-scale physics all SM couplings ● are marginal ● do not share global kinetic symmetries ● Gravity acts as anomalous dimension # TT < 0 relevant # TT > 0 SM . . . # TT < 0 Eichhorn & Held ‘17, 1705.02342 23
Linking electroweak- (IR) and Planck-scale physics all SM couplings ● are marginal ● do not share global kinetic symmetries ● Gravity acts as anomalous dimension # TT > 0 irrelevant # TT > 0 SM . . . # TT < 0 Phenomenological viability bound forbids # TT > 0 Eichhorn & Held ‘17, 1705.02342 23
Phenomenological viability bound Newton recall coupling cosmological constant higher curvature in tension with massive fermions In agreement with massive fermions Eichhorn & Held ‘17, 1705.02342 24
Preliminary: predictive power ● complex SU(2)-scalar ● left-handed SU(2)-doublet ● and two right-handed singlets charge conjugated 25
Preliminary: predictive power recall ● complex SU(2)-scalar ● left-handed SU(2)-doublet ● and two right-handed singlets charge conjugated Eichhorn & Held ‘17, 1705.02342 25
Preliminary: predictive power recall ● complex SU(2)-scalar ● left-handed SU(2)-doublet ● and two right-handed singlets charge conjugated g = 0 Eichhorn & Held ‘17, 1705.02342 25
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