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Register a new userFaddeev-Senjanovic Quantization of SU(n) N=2 Supersymmetric Gauge Field System with Non-Abelian Chern-Simons Topological Term and Its Fractional Spin
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Yong-Chang Huang ((1
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Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-abelian Chern-Simons topological term in 2+1 dimensions, and use consistency of a gauge condition naturally to deduce another gauge condition. Further, we get the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum has the orbital angular momentum and spin angular momentum of the non-abelian gauge field. Finally, we find out the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and the A_0^s (x) charge.
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According to the method of path integral quantization for the canonical constrained system in Faddeev-Senjanovic scheme, we quantize the supersymmetrical electrodynamic system in general situation, and obtain the generating functional of Green function. Another first class constraint is obtained by making the linear combination of several primary constraints, the generator of gauge transformation is constructed, gauge transformations of the all different fields are deduced. Utilizing the consistency equation of gauge fixing condition we deduce another gauge fixing condition, and we find that the secondary constraint of the system is an Euler-Lagrange equation that is just electro-charge conversation law. Thus, we do not need to calculate the other secondary constraints step by step, and get no new constraints naturally. So, the Faddeev-Senjanovic path integral quantization of the supersymmetrical electrodynamical system is simplified.
In supersymmetric (SUSY) field theory, there exist configurations which formally satisfy SUSY conditions but are not on original path integral contour. We refer to such configurations as complexified supersymmetric solutions (CSS). In this paper we discuss that CSS provide important information on large order behavior of weak coupling perturbative series in SUSY field theories. We conjecture that CSS with a bosonic (fermionic) free parameter give poles (zeroes) of Borel transformation of perturbative series whose locations are uniquely determined by actions of the solutions. We demonstrate this for various SUSY observables in 3d $mathcal{N}=2$ SUSY Chern-Simons matter theories on sphere. First we construct infinite number of CSS in general 3d $mathcal{N}=2$ SUSY theory with Lagrangian where adjoint scalar in vector multiplet takes a complex value and matter fields are nontrivial. Then we compare their actions with Borel transformations of perturbative expansions by inverse Chern-Simons levels for the observables and see agreement with our conjecture. It turns out that the CSS explain all the Borel singularities for this case.
We study $mathcal{N} = 3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the t Hooft large $N$ limit, we compute the exact $2 to 2$ scattering amplitudes of the fundamental scalar superfields to all orders in the t Hooft coupling $lambda$. Our computations are presented in $mathcal{N} = 1$ superspace and make significant use of the residual $SO(2)_R$ symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact $2 to 2$ scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the $mathcal{N} = 3$ theory in the planar limit is tree-level exact to all orders in the t Hooft coupling $lambda$. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.
Complete constraint analysis and choice of gauge conditions consistent with equations of motion is done for non-abelian Chern-Simons field interacting with N-component complex scalar field. Dirac-Schwinger condition is satisfied by the reduced phase-space Hamiltonian density with respect to the Dirac bracket.
We study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the t Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large $N$ ${cal N}=2$ supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general ${cal N} = 1$ supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of the t Hooft coupling.
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