We reformulate the Thirring model in $D$ $(2 \le D < 4)$ dimensions as a gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By virtue of such a gauge symmetry we can greatly simplify the analysis of the SD equation by taking the most appropriate gauge (``nonlocal gauge'') for the HLS. In the case of even-number of (2-component) fermions, we find the dynamical fermion mass generation as the second order phase transition at certain fermion number, which breaks the chiral symmetry but preserves the parity in (2+1) dimensions ($D=3$). In the infinite four-fermion coupling (massless gauge boson) limit in (2+1) dimensions, the result coincides with that of the (2+1)-dimensional QED, with the critical number of the 4-component fermion being $N_{\rm cr} = \frac{128}{3\pi^{2}}$. As to the case of odd-number (2-component) fermion in (2+1) dimensions, the regularization ambiguity on the induced Chern-Simons term may be resolved by specifying the regularization so as to preserve the HLS. Our method also applies to the (1+1) dimensions, the result being consistent with the exact solution. The bosonization mechanism in (1+1) dimensional Thirring model is also reproduced in the context of dual-transformed theory for the HLS.Comment: 33 page

It was found that deformation of S 7 gives rise to renormalization group(RG) flow from N = 8, SO(8)-invariant UV fixed point to N = 1, G 2 -invariant IR fixed point in four-dimensional gauged N = 8 supergravity. Also BPS supersymmetric domain wall configuration interpolated between these two critical points. In this paper, we use the G 2 -invariant RG flow equations for both scalar fields and domain wall amplitude and apply them to the nonlinear metric ansatz developed by de Wit, Nicolai and Warner some time ago. We carry out the M-theory lift of the G 2 -invariant RG flow through a combinatoric use of the four-dimensional RG flow equations and eleven-dimensional Einstein-Maxwell equations. The non-trivial r(that is the coordinate transverse to the domain wall)-dependence of vacuum expectation values makes the Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric RG flow connecting two critical points. By applying an ansatz for an eleven-dimensional threeform gauge field with varying scalars, we discover an exact solution to the eleven-dimensional Einstein-Maxwell equations corresponding to the M-theory lift of the G 2 -invariant RG flow.------E-mail addresses: ahn@knu.ac.kr (C. Ahn), taichi@hepth.hanyang.ac.kr (T. Itoh)

The compact 7-manifold arising in the compactification of 11-dimensional supergravity is described by the metric encoded in the vacuum expectation values(vevs) in d = 4, N = 8 gauged supergravity. Especially, the space of SU(3)-singlet vevs contains various critical points and RG flows(domain walls) developing along AdS 4 radial coordinate. Based on the nonlinear metric ansatz of de Wit-Nicolai-Warner, we show the geometric construction of the compact 7-manifold metric and find the local frames(siebenbeins) by decoding the SU(3)-singlet vevs into squashing and stretching parameters of the 7-manifold. Then the 11-dimensional metric for the whole SU(3)-invariant sector is obtained as a warped product of an asymptotically AdS 4 space with a squashed and stretched 7-sphere. We also discuss the difference in the 7-manifold between two sectors, namely SU(3) × U(1)-invariant sector and G 2 -invariant sector. In spite of the difference in base 6-sphere, both sectors share the 4-sphere of CP 2 associated with the common SU(3)-invariance of various 7-manifolds.------E-mail addresses: ahn@knu.ac.kr (C. Ahn), taichi@hepth.hanyang.ac.kr (T. Itoh)

We study dynamical symmetry breaking in three-dimensional QED with a Chern-Simons (CS) term, considering the screening effect of N flavor fermions. We find a new phase of the vacuum, in which both the fermion mass and a magnetic field are dynamically generated, when the coefficient of the CS term k equals Ne 2 ͞4p. The resultant vacuum becomes the finite-density state half filled by fermions. For k Ne 2 ͞2p, we find the fermion remains massless and only the magnetic field is induced. For k 0, spontaneous magnetization does not occur and should be regarded as an external field. [S0031-9007(98)06439-4] Field theoretical models in (2 1 1)-dimensional spacetime have attracted much attention as effective theories at long distance in planar condensed matter physics. Especially, quantum electrodynamics in 2 1 1 dimensions (QED 3 ) has been intensively studied in connection with the effective theories of high-T c superconductivity [1], as well as the probe for (3 1 1)-dimensional quantum chromodynamics. In 2 1 1 dimensions, there can be a topological gauge action known as Chern-Simons (CS) term. This term connects a magnetic field B with an electric charge density e͗c y c͘ for fermion field c. From this peculiar property, the CS term is used in the field theoretical understanding of the fractional quantum Hall effect [2].As a natural extension of QED 3 , a theory in which gauge field action includes both the CS term and the Maxwell term was proposed by Ref. [3]. In this theory (CS-QED 3 ), the coefficient k for the CS term gives the photon a gauge invariant mass which explicitly violates the parity symmetry. Some years ago, Hosotani [4] showed that spontaneous magnetization occurs in CS-QED 3 , through breaking the most secret symmetry-Lorentz invariance. In this theory, the Gauss law kB 2e͗c y c͘ follows from the equation of motion. Thus the magnetized vacuum corresponds to state with finite fermion density ͗c y c͘ fi 0. In Ref.[5] a chemical potential term m c y c was introduced as an explicit breaking term for Lorentz symmetry, and the condensation ͗c y c͘ at m ! 0 limit was studied. It was found that the above vacuum is stable if and only if the fermion bare mass is zero.In this paper, we examine the possibility that Lorentz symmetry is broken in a theory in which fermion mass and magnetization are both spontaneously generated. We regard the fermion bare mass term 2mcc as an explicit breaking term for flavor U͑2N͒ symmetry [6] as well as a chemical potential term m c y c for Lorentz symmetry. Solving the Schwinger-Dyson (SD) equation, we clarify whether or not two condensations, ͗c y c͘ and ͗cc͘, are dynamically realized at the symmetric limit m ! 0, m ! 0. They signal fermion mass generation and magnetization, respectively. For k Ne 2 ͞4p, we find a new phase of vacuum, in which both massive fermions and a magnetic field are dynamically generated so that both symmetries are simultaneously broken. The vacuum stability is also examined by calculating the Cornwall-Jackiw-Tomboulis (CJT) potential [7] and 2-loop effe...

We consider a hybrid of nonlinear sigma models in which two complex projective spaces are coupled with each other under a duality. We study the large N effective action in 1ϩ1 dimensions. We find that some of the dynamically generated gauge bosons acquire radiatively induced masses which, however, vanish along the self-dual points where the two couplings characterizing each complex projective space coincide. These points correspond to the target space of the Grassmann manifold along which the gauge symmetry is enhanced, and the theory favors the non-Abelian ultraviolet fixed point.