Adi Armoni

Comments on perturbative dynamics of non-commutative Yang–Mills theory

Abstract We study the U(N) non-commutative Yang–Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the θ→0 limit of the U(N) theory does not converge to the ordinary SU(N)×U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.

Exact results in non-supersymmetric large N orientifold field theories

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N).

Supersymmetry relics in one-flavor QCD from a new 1/N expansion

We suggest a new large-N(c) limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N(c)) QCD keeping quarks in the latter. We can then define a new 1/N(c) expansion (at a fixed number of flavors N(f)) that shares appealing properties with the topological (fixed N(f)/N(c)) expansion while being more suitable for theoretical analysis. In particular, for N(f)=1, our large-N(c) limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for N(f)=1 massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.

UV/IR mixing via closed strings and tachyonic instabilities

We discuss UV/IR mixing effects in non-supersymmetric non- commutative U(N) gauge theories. We show that the singular (nonplanar) terms in the 2- and 3-point functions, namely the poles and the logarithms, can be obtained from a manifestly gauge invariant effective action. The action, which involves open Wilson line operators, can be derived from closed strings exchange between two stacks of Dbranes. Our concrete example is type 0B string theory and the field theory that lives on a collection of N electric D3-branes. We show that one of the closed string modes that couple to the field theory operator which is responsible for the infrared poles, is the type 0 tachyon.

A Non-Supersymmetric Large-N 3D CFT And Its Gravity Dual

We propose a three dimensional non-supersymmetric theory that is conformal in the large N limit. In a certain well defined bosonic sub-sector of gauge invariant operators, this theory is planar equivalent to the theory recently proposed by Aharony, Bergman, Jafferis and Maldacena as the theory on multiple M2 branes at an orbifold singularity. We discuss the realization of the theory on a brane configuration of type 0B string theory. Moreover, we propose an 11D gravity dual, obtained by a projection of M-theory on AdS4 × S7/Zk.

Refining the proof of planar equivalence

We outline a full non-perturbative proof of planar (large-N) equivalence between bosonic correlators in a theory with Majorana fermions in the adjoint representation and one with Dirac fermions in the two– index (anti)symmetric representation. In a particular case (one flavor), this reduces to our previous result — planar equivalence between super-Yang–Mills theory and a non-supersymmetric “orientifold field theory.” The latter theory becomes one-flavor massless QCD at N = 3.

Supersymmetry Relics in One-Flavor QCD from a New1/NExpansion

We suggest a new large-N(c) limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N(c)) QCD keeping quarks in the latter. We can then define a new 1/N(c) expansion (at a fixed number of flavors N(f)) that shares appealing properties with the topological (fixed N(f)/N(c)) expansion while being more suitable for theoretical analysis. In particular, for N(f)=1, our large-N(c) limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for N(f)=1 massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.

Non-tachyonic type 0B orientifolds, non-supersymmetric gauge theories and cosmological RG flow

Abstract We discuss gauge theories on D3 branes embedded in special non-tachyonic orientifolds of the 0B string theory. In general, they correspond to non-supersymmetric SU(N) gauge theories with scalars in the adjoint representation and spinors in the (anti-)symmetric representation. We study these theories via the AdS/CFT correspondence and present evidence of their relation to N =4 SYM in the planar limit. We also discuss finite N properties, focusing in particular on the renormalization group flow. Up to two loops, the logarithmic running of the gauge coupling is described by the dilaton tadpole and the cosmological constant that naturally emerge on the string theory side.

On non-commutative super Yang–Mills

Abstract We discuss the Seiberg–Witten solution of the non-commutative N =2 U ( N ) SYM model. The solution is described in terms of the ordinary Seiberg–Witten curve of the SU ( N ) theory plus an additional free U (1). Hence, at the two-derivative approximation the theory flows to the ordinary commutative theory in the infrared ( k θ ). In particular, the center U (1) is free and it decouples from the other U (1)s. In addition, no UV/IR mixing is found.

Rotating Strings in Confining AdS/CFT Backgrounds

We study semiclassical rotating strings in AdS/CFT backgrounds that exhibit both confinement and finite-size effects. The energy versus spin dispersion relation for short strings is the expected Regge trajectory behaviour, with the same string tension as is measured by the Wilson loop. Long strings probe the interplay between confinement and finite-size effects. In particular, the dispersion relation for long strings shows a characteristic dependence on the string tension and the finite-size scale.