Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA

We investigate the S3 free energy of $$ \mathcal{N} $$ N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N)r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = − log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal $$ \frac{1}{6} $$ 1 6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter

We consider Chern-Simons theory coupled to massive fundamental matter in three spacetime dimensions at finite temperature, in the large N limit. We compute several thermal correlators in this theory for both fermionic and bosonic matter separately. The results are computed in the large N ’t Hooft limit but for arbitrary values of the ’t Hooft coupling. Furthermore, we generalize the computations of the four-point function of fundamental scalars in the bosonic theory to finite temperature. As a consistency check, we see that the results obtained here agree with the existing previous results in different limiting cases. Moreover, we check that the results are consistent with the conjectured bosonization duality, providing an additional evidence of it.

Differential Dyson–Schwinger equations for quantum chromodynamics

Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

Three-point functions in the 𝒩 = 4 orthogonal coset theory

We construct the lowest higher spin-2 current in terms of the spin-1 and the spin-[Formula: see text] currents living in the orthogonal [Formula: see text] Wolf space coset theory for general [Formula: see text]. The remaining 15 higher spin currents are determined. We obtain the three-point functions of bosonic (higher) spin currents with two scalars for finite [Formula: see text] and [Formula: see text] (the level of the spin-1 current). By multiplying [Formula: see text] into the above Wolf space coset theory, the other 15 higher spin currents together with the above lowest higher spin-2 current are realized in the extension of the large [Formula: see text] linear superconformal algebra. Similarly, the three-point functions of bosonic (higher) spin currents with two scalars for finite [Formula: see text] and [Formula: see text] are obtained. Under the large [Formula: see text] ’t Hooft limit, the two types of three-point functions in the nonlinear and linear versions coincide as in the unitary coset theory found previously.

THE CHIRAL CONDENSATE OF STRONGLY COUPLED QCD IN THE 't HOOFT LIMIT

Using the recently proposed generalization to an arbitrary number of colors of the strong coupling approach to lattice gauge theories,1 we compute the chiral condensate of massless QCD in the 't Hooft limit.