The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice

Hietanen, Ari; Narayanan, Rajamani

doi:10.1007/jhep01(2010)079

Cited by 31 publications

(27 citation statements)

References 24 publications

(33 reference statements)

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“…Lattice simulations with one-site or few-site large-N matrix models confirm this proposal [40][41][42], as does an earlier simulation with massive adjoint fermions [39], emulating R 3 × S 1 at N = 3. In the end, the resolution is a simple realization.…”

Section: Boundary Conditions As An Idea and Center Stability In Qcd(supporting

confidence: 70%

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Dunne

Ünsal

2016

Annu. Rev. Nucl. Part. Sci.

112

170

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We present a broad conceptual introduction to some new ideas in non-perturbative QFT. The large-N orbifold-orientifold equivalence connects a natural large-N limit of QCD to QCD with adjoint fermions. QCD(adj) with periodic boundary conditions and double-trace deformation of Yang-Mills theory satisfy large-N volume independence, a type of orbifold equivalence. Certain QFTs that satisfy volume independence at N = ∞ exhibit adiabatic continuity at finite-N , and also become semi-classically calculable on small R 3 × S 1 . We discuss the role of monopole-instantons, and magnetic and neutral bion saddles in connection to mass gap, and center and chiral symmetry realizations. Neutral bions also provide a weak coupling semiclassical realization of infrared-renormalons. These considerations help motivate the necessity of complexification of path integrals (Picard-Lefschetz theory) in semi-classical analysis, and highlights the importance of hidden topological angles. Finally, we briefly review the resurgence program, which potentially provides a novel non-perturbative continuum definition of QFT. All these ideas are continuously connected.Keywords: large-N orbifold and orientifold equivalence, volume independence, double-trace deformations, adiabatic continuity, semi-classical calculability, magnetic and neutral bions, Picard-Lefschetz theory of path integration, and resurgence arXiv:1601.03414v1 [hep-th]

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Section: Boundary Conditions As An Idea and Center Stability In Qcd(supporting

confidence: 70%

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Dunne

Ünsal

2016

Annu. Rev. Nucl. Part. Sci.

112

170

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“…The Euclidean partition function with periodic fermions on a circle of circumference L corresponds to a twisted (non-thermal) partition function, Z(L) = tr[e −LH (−1) F ], where H is the gauge theory Hamiltonian and F is fermion number. For supersymmetric theories, like QCD(adj) with n f = 1, this is the Witten index [4] which is famously independent JHEP08(2012)063 of L. Recent work has shown that there are also non-supersymmetric gauge theories, like SU(N ) QCD(adj) with n f > 1 and with large-enough N , which do not undergo any phase transition as the radius of the circle is varied [5][6][7]. This is due to large-N volume independence: at large N an SU(N ) gauge theory on R 4 is non-perturbatively equivalent to its compactified version on T d × R 4−d , where T d is a d-dimensional torus, provided center and translation symmetries are unbroken [1,8].…”

Section: Introduction and Resultsmentioning

confidence: 99%

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

Argyres

Ünsal

2012

J. High Energ. Phys.

176

319

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Abstract:We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics -which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription -to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries andÉcalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.

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“…the finite temperature case), the theory is confining at an arbitrarily small radius and the condition for volume reduction is satisfied. Following their work several papers [5][6][7][8][9][10][11][12][13][14][15][16][17] supporting the validity of volume reduction for theories with adjoint fermions were published. This observation becomes particularly interesting when combined with…”

Section: Introductionmentioning

confidence: 99%

k-string tension from Eguchi-Kawai reduction

Armoni

Dorigoni

Veneziano

2011

J. High Energ. Phys.

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The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice

Cited by 31 publications

References 24 publications

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

k-string tension from Eguchi-Kawai reduction

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