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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.
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
Four-graviton couplings in the low energy effective action of type II string vacua compactified on tori are strongly constrained by supersymmetry and U-duality. While the $R^4$ and $D^4 R^4$ couplings are known exactly in terms of Langlands-Eisenstei
Tensoring two on-shell super Yang-Mills multiplets in dimensions $Dleq 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $mathbb{D}$ with each dimension $3leq
A calculation of the renormalization group improved effective potential for the gauged U(N) vector model, coupled to $N_f$ fermions in the fundamental representation, computed to leading order in 1/N, all orders in the scalar self-coupling $lambda$,
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