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.
We investigate effects of field theory instantons by considering D-instantons in a suitable D3-brane background. In supersymmetric QCD with SU (N c ) gauge group with N f = N c flavors, the moduli space of vacua is deformed by instantons. This effect can be described by the chiral interactions which are called multi-fermion F -terms. We derive these chiral interaction terms as D-instanton effects in the presence of D3-branes. For SU (2), the obtained result agrees with the previous result worked out by Beasley and Witten [1]. We also explicitly work out those for the case of the symplectic gauge group, and show that they describe the deformation of the moduli space.
We develop a method to compute the one-loop effective action of noncommutative U (1) gauge theory based on the bosonic worldline formalism, and derive compact expressions for N -point 1PI amplitudes. The method, resembling perturbative string computations, shows that open Wilson lines emerge as a gauge invariant completion of certain terms in the effective action. The terms involving open Wilson lines are of the form reminiscent of closed string exchanges between the states living on the two boundaries of a cylinder. They are also consistent with recent matrix theory analysis and the results from noncommutative scalar field theories with cubic interactions.
We explicitly construct cubic interaction light-cone Hamiltonian for the chiral primary system involving the metric fields and the self-dual four-form fields in the IIB pp-wave supergravity. The background fields representing pp-waves exhibit SO(4) ⊥ ×SO(4) × Z 2 invariance. It turns out that the interaction Hamiltonian is precisely the same as that for the dilaton-axion system, except for the fact that the chiral primary system fields have the opposite parity to that of the dilaton-axion fields under the Z 2 transformation that exchanges two SO(4)'s.While the IIB string theory in flat space-time exhibits SO(8) invariance, pp-wave backgrounds of Refs. [1,2] possess SO(4) ⊥ ×SO(4) × Z 2 invariance. The consequence of this fact at the level of supergravity spectrum is that there are two extra scalars s and s under SO(4) ⊥ × SO(4) on top of the dilaton and axion that are scalars under SO (8) (τ andτ with the energy m 2 = 4f ). They come from the trace part of the SO(4) ⊥ subspace metric, that is related to the SO(4) subspace metric via the SO(8) traceless condition, and the four-form RR gauge field along the SO(4) ⊥ , which is related to the SO(4) part through the self-duality condition. At the free theory level, it is known that they combine to produce chiral primary with m 2 = 0 and anti-chiral primary with m 2 = 8f [3]. Recalling that the Z 2 part of the symmetry is an element of the SO (8) that exchanges SO(4) ⊥ and SO(4) , the dilaton and axion, being SO(8) scalars, have even parity under the Z 2 . When viewed from this angle, chiral primaries should have odd parity. The confirmation of this expectation at the supergravity interaction level is the purpose of this paper. Specifically, we construct the cubic interaction part of the light-cone Hamiltonian for the chiral primary system starting from the covariant IIB supergravity.It turns out that thus obtained interaction Hamiltonian is precisely the same as that for the dilaton-axion system [4,5], except for the fact that s ands (τ andτ ) have odd (even) parity under the exchange of the two SO(4) ′ s 1 . This result is interesting at least from two perspectives. First, in view of the apparent difference in the SO(8) tensor structure of the two systems, this agreement is not entirely trivial. Generically, the treatment of the self-dual four-form fields in curved backgrounds is a non-trivial problem [7], but the pp-wave backgrounds provide us with a tractable setting. Secondly, the ground state 2 of the string theory in pp-wave backgrounds should be given odd parity; supergravity can be obtained from string theory via a smooth deformation of parameters, and the discrete charge assignment should not change under this deformation.The bosonic sector of type IIB supergravity involves a dilaton, an axion, a graviton, two antisymmetric 2-form fields, and a self-dual antisymmetric four-form field. We are interested in the system of the gravity field g µν and the self-dual antisymmetric 4-form 1 See [6] for related discussions. 2 In the string field theory side [8,9], this...
We investigate the enlarged CP(N) model in 2+1 dimensions. This is a hybrid of two CP(N) models coupled with each other in a dual symmetric fashion, and it exhibits the gauge symmetry enhancement and radiative induction of the finite off-diagonal gauge boson mass as in the 1+1 dimensional case. We solve the mass gap equations and study the fixed point structure in the large-N limit. We find an interacting ultraviolet fixed point which is in contrast with the 1+1 dimensional case. We also compute the large-N effective gauge action explicitly.
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