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Register a new userGauge Symmetry Enhancement and Radiatively Induced Mass in the Large N Nonlinear Sigma Model
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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 1+1 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.
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We compute the free energy in the presence of a chemical potential coupled to a conserved charge in the effective SU(N)xSU(N) scalar field theory to third order for asymmetric volumes in general d-dimensions, using dimensional regularization. We also compute the mass gap in a finite box with periodic boundary conditions.
Considering marginally relevant and relevant deformations of the weakly coupled $(3+1)$-dimensional large $N$ conformal gauge theories introduced in arXiv:2011.13981, we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the $Nrightarrowinfty$ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. In certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global $mathbb Z_2$ or $U(1)$ symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the masses (squared) added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the $Nrightarrowinfty$ limit.
This is a brief introductory review of the AdS/CFT correspondence and of the ideas that led to its formulation. Emphasis is placed on dualities between conformal large $N$ gauge theories in 4 dimensions and string backgrounds of the form $AdS_5times X_5$. Attempts to generalize this correspondence to asymptotically free theories are also included.
We analyze the two-dimensional CP(N-1) sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique phase, which smoothly approaches in the large L limit the standard 2D CP(N-1) sigma model in confinement phase, with a constant mass generated for the n(i) fields. We study the full functional saddle-point equations for finite L, and solve them numerically. The latter reduces to the well-known gap equation in the large L limit. It is found that the solution satisfies actually both the Dirichlet and Neumann conditions.
We holomorphically embed nonlinear sigma models (NLSMs) on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ in the hyper-K{a}hler (HK) NLSM on the cotangent bundle of the Grassmann manifold $T^ast G_{2N,N}$, which is defined by $G_{N+M,M}=frac{SU(N+M)}{SU(N)times SU(M)times U(1)}$, in the ${mathcal{N}}=1$ superspace formalism and construct three-pronged junctions of the mass-deformed NLSMs (mNLSMs) in the moduli matrix formalism (MMF) by using a recently proposed method.
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