General gauge-Yukawa-quartic β-functions at 4-3-2-loop order

We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa β-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the β-functions, we compare the general form to the specific β-functions of known theories to constrain the unknown coefficients. The Weyl consistency conditions provide additional constraints, completing the determination.

Gradient flow and holography from a local Wilsonian cutoff

We consider the vacuum partition function of a 4d scalar QFT in a curved background as function of bare marginal and relevant couplings. A local UV cutoff $$\Lambda (x)$$ Λ ( x ) transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms including Wilsonian cutoff functions. The local cutoff can be absorbed completely by a rescaling of the metric and the bare couplings. The vacuum partition function satisfies consistency conditions which follow from the Abelian nature of local redefinitions of the cutoff, and which differ from Weyl rescalings. These imply a gradient flow for beta functions describing the cutoff dependence of rescaled bare couplings. The consistency conditions allow to satisfy all but one Hamiltonian constraints required for a holographic description of the flow of bare couplings with the cutoff.

Generalised holonomies and K(E9)

The involutory subalgebra K($$ \mathfrak{e} $$ e 9) of the affine Kac-Moody algebra $$ \mathfrak{e} $$ e 9 was recently shown to admit an infinite sequence of unfaithful representations of ever increasing dimensions [1]. We revisit these representations and describe their associated ideals in more detail, with particular emphasis on two chiral versions that can be constructed for each such representation. For every such unfaithful representation we show that the action of K($$ \mathfrak{e} $$ e 9) decomposes into a direct sum of two mutually commuting (‘chiral’ and ‘anti-chiral’) parabolic algebras with Levi subalgebra $$ \mathfrak{so} $$ so (16)+ ⊕ $$ \mathfrak{so} $$ so (16)−. We also spell out the consistency conditions for uplifting such representations to unfaithful representations of K($$ \mathfrak{e} $$ e 10). From these results it is evident that the holonomy groups so far discussed in the literature are mere shadows (in a Platonic sense) of a much larger structure.

Integrable bootstrap for AdS3/CFT2 correlation functions

We propose an integrable bootstrap framework for the computation of correlation functions for superstrings in AdS3 × S3 × T4 backgrounds supported by an arbitrary mixture or Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. The framework extends the “hexagon tessellation” approach which was originally proposed for AdS5 × S5 and for the first time it demonstrates its applicability to other (less supersymmetric) setups. We work out the hexagon form factor for two-particle states, including its dressing factors which follow from those of the spectral problem, and we show that it satisfies non-trivial consistency conditions. We propose a bootstrap principle, slightly different from that of AdS5 × S5, which allows to extend the form factor to arbitrarily many particles. Finally, we compare its predictions with some correlation functions of protected operators. Possible applications of this construction include the study of wrapping corrections, of higher-point correlation functions, and of non-planar corrections.

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

In this paper, we study the -gravitation theory under the assumption that the standard matter-energy content of the universe is a perfect fluid with linear barotropic equation of state within the framework of Bianchi-Type III model from the class of homogeneous and anisotropic universe models. However, whether such a restriction lead to any contradictions or inconsistencies in the field equations will create an issue that needs to be examined. Under the effective fluid approach, we will be concerned mainly the field equations in an orthonormal tetrad framework with an equimolar and examined the situation of establishing the functional form of together with the scale factors, which are their solutions. Unlike similar studies, which are very few in the literature, instead of assuming preliminary solutions, we determined the consistency conditions of the field equations by assuming the matter energy content of the universe as an isotropic perfect fluid for Bianchi-Type III.

8d supergravity, reconstruction of internal geometry and the Swampland

We sharpen Swampland constraints on 8d supergravity theories by studying consistency conditions on worldvolume theory of 3-brane probes. Combined with a stronger form of the cobordism conjecture, this leads to the reconstruction of the compact internal geometry and implies strong restrictions on the gauge algebra and on some higher derivative terms (related to the level of the current algebra on the 1-brane). In particular we argue that 8d supergravity theories with $$ {\mathfrak{g}}_2 $$ g 2 gauge symmetry are in the Swampland. These results provide further evidence for the string lamppost principle in 8d with 16 supercharges.

Holographic correlators at finite temperature

We consider weakly-coupled QFT in AdS at finite temperature. We compute the holographic thermal two-point function of scalar operators in the boundary theory. We present analytic expressions for leading corrections due to local quartic interactions in the bulk, with an arbitrary number of derivatives and for any number of spacetime dimensions. The solutions are fixed by judiciously picking an ansatz and imposing consistency conditions. The conditions include analyticity properties, consistency with the operator product expansion, and the Kubo-Martin-Schwinger condition. For the case without any derivatives we show agreement with an explicit diagrammatic computation. The structure of the answer is suggestive of a thermal Mellin amplitude. Additionally, we derive a simple dispersion relation for thermal two-point functions which reconstructs the function from its discontinuity.