Does massless QCD have vacuum energy?

Holdom, Bob

doi:10.1088/1367-2630/10/5/053040

Cited by 12 publications

(19 citation statements)

References 35 publications

(37 reference statements)

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“…Holdom [55] has raised the question of whether the vacuum energy in massless QCD could in fact vanish. This is in part because the present lattice estimates are uncertain enough to include a vanishing value.…”

Section: More General Resultsmentioning

confidence: 99%

Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

Donoghue

Menezes

2018

Phys. Rev. D

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We discuss a variation of quadratic gravity in which the gravitational interaction remains weakly coupled at all energies, but is assisted by a Yang-Mills gauge theory which becomes strong at the Planck scale. The Yang-Mills interaction is used to induce the usual Einstein-Hilbert term, which was taken to be small or absent in the original action. We study the spin-two propagator in detail, with a focus on the high mass resonance which is shifted off the real axis by the coupling to real decay channels. We calculate scattering in the J ¼ 2 partial wave and show explicitly that unitarity is satisfied. The theory will in general have a large cosmological constant and we study possible solutions to this, including a unimodular version of the theory. Overall, the theory satisfies our present tests for being a ultraviolet completion of quantum gravity.

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Section: More General Resultsmentioning

confidence: 99%

Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

Donoghue

Menezes

2018

Phys. Rev. D

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“…However, the value of the gluon condensage is not firmly known. Indeed, Holdom has given arguments that the gluon condensate could vanish, drawing attention to the absence of both experimental and theoretical evidence for a nonvanishing gluon condensate in massless QCD [19]. Some of the difficulty in direct lattice calculations is the presence of a dimensionful cut-off for the lattice, and also disentangling the gluonic contribution from that of massive quarks.…”

Section: Discussionmentioning

confidence: 99%

Inducing the Einstein action in QCD-like theories

Donoghue

Menezes

2018

Phys. Rev. D

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“…The left-and right-handed Weyl fermions, ψ − (x) and ψ + (x), are assumed in 4, the fourdimensional irreducible spinor representation of SO (6). The generators of the spinor representation of SO(6), i.e.…”

Section: Limit Of the Large Majorana-type Yukawa-coupling/mass Termsmentioning

confidence: 99%

“…Chiral gauge theories have several interesting possibilities in their own dynamics: fermion number non-conservation due to chiral anomaly [1,2], various realizations of the gauge symmetry and global flavor symmetry [3,4], the existence of massless composite fermions suggested by 't Hooft's anomaly matching condition [5], the classical scale invariance and the vanishing vacuum energy [6,7] and so on. Unfortunately, little is known so far about the actual behavior of chiral gauge theories beyond perturbation theory.…”

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confidence: 99%

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

Kikukawa

2019

Progress of Theoretical and Experimental Physics

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It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg-Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions and therefore having the simpler fermion path-integral measure, it has been argued that the mirror fermions do not decouple: in the 345 model with Dirac-and Majorana-Yukawa couplings to XY-spin field, the twopoint vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the PMS phase. We re-examine why the attempt seems a "Mission: Impossible" in the 345 model. We point out that the effective operators to break the fermion number symmetries ('t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature. We then consider a simpler four-flavor axial gauge model, the 1 4 (-1) 4 model, in which the U(1) A gauge and Spin(6)( ∼ = SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior, and we still argue that all you need is killing the continuous mirror-fermion symmetries with would-be gauge anomalies non-matched. Finally, by gauging a U(1) subgroup of the U(1) A × Spin(6)(SU(4)) of the previous model, we formulate the 21(−1) 3 chiral gauge model and argue that the induced fermion measure term satisfies the required locality property and provides a solution to the reconstruction theorem. This gives us "A New Hope" for the mission to be accomplished.An explicit example of such lattice Dirac operator is given by the overlap Dirac operator [17,19], which was derived by Neuberger from the overlap formalism [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. 2 By the Ginsparg-Wilson relation, it is possible to realize an exact chiral symmetry on the lattice [44] in the manner consistent with the no-go theorem. [45][46][47][48][49] It is also possible to introduce Weyl fermions on the lattice and this opens the possibility to formulate anomaly-free chiral gauge theories on the lattice [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]. In the case of U(1) chiral gauge theories, Lüscher[50] proved rigorously that it ...

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Does massless QCD have vacuum energy?

Cited by 12 publications

References 35 publications

Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

Inducing the Einstein action in QCD-like theories

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

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