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Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we arrive to the partition function of a $U(1)$ gauge theory coupled to a scalar field with an action that exhibits a Dirac monopole solution. A subsequent reduction to $d=2$ dimensions leads to the partition function of a theory in which the gauge field decouples from two scalars which have non-trivial vortex-like solutions. Finally this $d=2$ partition function can be related to the bosonized version of the two-dimensional QED$_2$ (Schwinger) model.
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We study behaviour of the critical $O(N)$ vector model with quartic interaction in $2 leq d leq 6$ dimensions to the next-to-leading order in the large-$N$ expansion. We derive and perform consistency checks that provide an evidence for the existence of a non-trivial fixed point and explore the corresponding CFT. In particular, we use conformal techniques to calculate the multi-loop diagrams up to and including 4 loops in general dimension. These results are used to calculate a new CFT data associated with the three-point function of the Hubbard- Stratonovich field. In $6-epsilon$ dimensions our results match their counterparts obtained within a proposed alternative description of the model in terms of $N+1$ massless scalars with cubic interactions. In $d=3$ we find that the OPE coefficient vanishes up to $mathcal{O}(1/N^{3/2})$ order.
We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the $varepsilon$-expansion.
We consider Quantum Electrodynamics with an even number $N_f$ of bosonic or fermionic flavors, allowing for interactions respecting at least $U(N_f/2)^2$ global symmetry. Both in the bosonic and in the fermionic case, we find four interacting fixed points: two with $U(N_f/2)^2$ symmetry, two with $U(N_f)$ symmetry. Large $N_f$ arguments suggest that, lowering $N_f$, all these fixed points merge pairwise and become complex CFTs. In the bosonic QEDs the merging happens around $N_fsim 9{-}11$ and does not break the global symmetry. In the fermionic QEDs the merging happens around $N_fsim3{-}7$ and breaks $U(N_f)$ to $U(N_f/2)^2$. When $N_f=2$, we show that all four bosonic fixed points are one-to-one dual to the fermionic fixed points. The merging pattern suggested at large $N_f$ is consistent with the four $N_f=2$ boson $lra$ fermion dualities, providing support to the validity of the scenario.
We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The $U(2)$ ultraviolet global symmetry is often enhanced in the infrared, for instance to $O(4)$ or $SU(3)$. This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the $D = 4 - varepsilon$ expansion shows that the $U(2)$ preserving superpotential deformations of the sQED (modulo tuning mass terms to zero) are irrelevant, so the fixed points with enhanced symmetry are stable. We also construct an example of $mathcal{N} = 2$ sQED with 4 flavors that exhibits enhanced $SO(6)$ symmetry.
Oscillons are long-lived, slowly radiating solutions of nonlinear classical relativistic field theories. Recently it was discovered that in one spatial dimension their decay may proceed in staccato bursts. Here we perform a systematic numerical study to demonstrate that although this behaviour is not confined to one spatial dimension, it quickly becomes unobservable when the dimension of space is increased. To complete the picture we also present explicit results on the dimension dependence of the collapse instability observed for three-dimensional oscillons.
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