Tadahito Nakajima

Nonplanar anomalies in noncommutative gauge theories with adjoint matter fields

Using path integral method (Fujikawa’s method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representation. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit p̃μ(≡ θpν) → 0. The adjoint chiral fermion carries no anomaly in non-planar sector in D = 4k(k = 1, 2, . . . , ) dimensions. It is naturally shown from the path integral method that anomalies in non-planar sector originate in UV/IR mixing. ∗E-mail address: nakajima@phys.ge.cst.nihon-u.ac.jp

Conformal anomalies in noncommutative gauge theories

We calculate conformal anomalies in noncommutative gauge theories by using the path integral method (Fujikawas method). Along with the axial anomalies and chiral gauge anomalies, conformal anomalies take the form of the straightforward Moyal deformation in the corresponding conformal anomalies in ordinary gauge theories. However, the Moyal star product leads to the difference in the coefficient of the conformal anomalies between noncommutative gauge theories and ordinary gauge theories. The

Glueball mass spectra for supergravity duals of noncommutative gauge theories

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Chiral symmetry restoration in holographic noncommutative QCD

(Callan-Symanzik) functions which are evaluated from the coefficient of the conformal anomalies coincide with the result of perturbative analysis.

D1/D5 system and Wilson loops in (non)commutative gauge theories

We derive the glueball masses in noncommutative super Yang-Mills theories in four dimensions via the dual supergravity description. The spectrum of glueball masses is discrete due to the noncommutativity and the glueball masses are proportional to the noncommutativity parameter with dimension of length. The mass spectrum in the WKB approximation closely agrees with the mass spectrum in finite temperature Yang-Mills theory.

Local gauge fields based on a Yang-Mills theory in loop space

We consider the noncommutative deformation of the Sakai-Sugimoto model at finite temperature and finite baryon chemical potential. The space noncommutativity is possible to have an influence on the flavor dynamics of the QCD. The critical temperature and critical value of the chemical potential are modified by the space noncommutativity. The influence of the space noncommutativity on the flavor dynamics of the QCD is caused by the Wess-Zumino term in the effective action of the D8-branes. The intermediate temperature phase, in which the gluons deconfine but the chiral symmetry remains broken, is easy to be realized in some region of the noncommutativity parameter.

LOCAL GAUGE FIELDS BASED ON A U(1) GAUGE THEORY IN LOOP SPACE

Abstract We study the behavior of the Wilson loop in the (5+1)-dimensional supersymmetric Yang–Mills theory with the presence of the solitonic object. Using the dual string description of the Yang–Mills theory that is given by the D1/D5 system, we estimate the Wilson loops both in the temporal and spatial cases. For the case of the temporal loop, we obtain the velocity dependent potential. For the spatial loop, we find that the area law is emerged due to the effect of the D1-branes. Further, we consider D1/D5 system in the presence of the constant B field. It is found that the Wilson loop obeys the area law for the effect of the noncommutativity.

A U(1) Gauge Theory for Antisymmetric Tensor Fields

We construct a Yang–Mills theory in loop space (the space of all loops in Minkowski space) with the Kac–Moody gauge group in such a way that the theory possesses reparametrization invariance. On the basis of the Yang–Mills theory, we derive the usual Yang–Mills theory and a non-Abelian Stueckelberg formalism extended to local antisymmetric and symmetric tensor fields of the second rank. The local Yang–Mills field and the second-rank tensor fields are regarded as components of a Yang–Mills field on the loop space.

THE SPECTRUM OF LOW SPIN MESONS AT FINITE TEMPERATURE IN HOLOGRAPHIC NONCOMMUTATIVE QCD

We present a U(1) gauge theory defined in loop space, the space of all loops in Minkowski space. On the basis of the U(1) gauge theory, we derive a local field theory of the second-rank antisymmetric tensor field (Kalb-Ramond field) and the Stueckelberg formalism for a massive vector field; the second-rank antisymmetric tensor field and the massive vector field are regarded as parts of a U(1) gauge field on the loop space. We also consider the quantum theories of the second-rank antisymmetric tensor field and the massive vector field on the basis of a BRST formalism for the U(1) gauge theory in loop space. In addition, reparametrization invariance in the U(1) gauge theory is discussed in detail.

A Yang-Mills Theory in Loop Space and Generalized Chapline-Manton Coupling

We show that a U(1) gauge theory defined in the configuration space for closed p-branes yields the gauge theory of a massless rank-(p+1) antisymmetric tensor field and the Stueckelberg formalism for a massive vector field.