arXiv subjects

Giacomo Santoni

Publications and source records attributed to Giacomo Santoni.

6 recordsLinked to original sources

arXiv2026

Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group

Extensive systems have a simple thermodynamic signature: the dimensionless canonical free energy scales homogeneously with the size of the system. We show that the failure of this scaling, measured by the replica energy ${\cal E}$, provides a useful bridge between statistical mechanics and quantum field theory. The associated differential operator $(1-\frac1d L\partial_L)$ removes the leading bulk contribution to $\mathcal{F}=βF_{\rm can}=-\log Z$ and isolates the part that is sensitive to boundaries, topology, defects, long-range forces, or other sources of nonadditivity. In quantum field theory this thermodynamic idea has two closely related uses. For ordinary finite-volume or spherical partition functions, suitable higher-order versions of the same filter remove local counterterms and extract universal fixed-point data such as the central charge, the sphere free energy $F$, and the Euler anomaly coefficient $a$. For replica geometries with entangling defects, the same filtering principle gives the renormalized defect free energy. In $2+1$ dimensions, its $n\to1$ limit gives the entropic $F$-function, with the sign fixed below by the standard free-energy convention. We use this perspective to distinguish ordinary finite-size corrections, topology-dependent constants in gapped phases, subextensive fracton degeneracies, and genuinely nonextensive systems with long-range interactions such as self-gravitating thermal matter. Replica energy therefore offers a common thermodynamic language for additivity, defect free energies, and renormalization-group irreversibility.

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arXiv2026

The scheme independent 3-sphere free energy is not a monotone F-function

We study the natural scheme-independent quantity obtained from the three-sphere partition function of a $(2+1)$-dimensional quantum field theory by removing all local counterterm ambiguities. At conformal fixed points this quantity equals the standard $F$-theorem invariant. Conformal perturbation theory shows that it locally decreases at $O(g^2)$ under any relevant scalar deformation of a three-dimensional CFT. However, an exact analysis of the free massive scalar on $S^3$ shows that this sphere-free-energy interpolant is not monotone along the full renormalization-group flow: it dips below its infrared value and then returns to it. Thus the natural counterterm-subtracted quantity built from sphere thermodynamics is not, by itself, a monotone $F$-function. We trace the obstruction to the second-order differential operator required to eliminate the local ambiguities.

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arXiv2026

Baryons, Skyrmions and $θ$-periodicity anomaly in chiral and vector-like gauge theories

In this paper, we study the baryons and solitons of chiral and vector-like $SU(N)$ gauge theories with matter in mixed one and two-index representations. Focusing on the Color-flavor locked (CFL) phase, we compute the topology of the coset of their low-energy EFT. We find that in the chiral models under consideration, Skyrmions are always absent. We also show, however, that some of these models admit heavy baryons that are expected to be stable, because their decay into the lighter degrees of freedom of the EFT is forbidden by the unbroken symmetry group. This mismatch suggests that some deeper dynamical mechanism must be responsible with either the instability of the seemingly stable heavy baryons or the unreliability of the Skyrme model in the low-energy EFT. In the vector-like models all the expected baryons are mirrored by Skyrmions. Then we turn to the study of domain walls. We determine some aspects of their dynamics by matching the $θ$-periodicity anomaly. We find that, for complete CFL, the $θ$-periodicity anomaly is always matched without introducing new dynamical degrees of freedom in the low-energy EFT. If part of the color group is unbroken, new dynamical degrees of freedom must be added to the low-energy EFT in the domain-wall background with few exceptions.

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arXiv2025

Twistor Wilson loops in large-$N$ Yang-Mills theory

It has been known for many years that, in Yang-Mills theories with $\mathcal{N}=4,2,2^*$ supersymmetry, certain nontrivial supersymmetric Wilson loops exist with v.e.v. either trivial or computable by localization that arises from a cohomological field theory, which also computes the nonperturbative prepotential in $\mathcal{N}=2,2^*$ theories. Moreover, some years ago it has been argued that, in analogy with the supersymmetric case, certain nontrivial twistor Wilson loops with trivial v.e.v. to the leading large-$N$ order exist in pure SU($N$) Yang-Mills theory and are computed, to the leading large-$N$ order, by a topological field/string theory that, to the next-to-leading $\frac{1}{N}$ order, conjecturally captures nonperturbative information on the glueball spectrum and glueball one-loop effective action as well. In fact, independently of the above, it has also been claimed that "every gauge theory with a mass gap should contain a possibly trivial topological field theory in the infrared", so that the aforementioned twistor Wilson loops realize a stronger version of this idea, as they have trivial v.e.v. at all energy scales and not only in the infrared. In the present paper, we provide a detailed proof of the triviality of the v.e.v. of twistor Wilson loops at the leading large-$N$ order in Yang-Mills theory that has previously been only sketched, opening the way to further developments.

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arXiv2025

Superfield twist-$2$ operators in $\mathcal{N} = 1$ SCFTs and their renormalization-group improved generating functional in $\mathcal{N} = 1$ SYM theory

We provide a new construction of superfield collinear twist-$2$ operators as infinite-dimensional, irreducible representations of the collinear superconformal algebra in $\mathcal{N}=1$ superconformal field theories. As an application, we realize the above representations in terms of free superfields, in a manifestly gauge-invariant and supersymmetric-covariant fashion, in the zero coupling limit of $\mathcal{N}=1$ supersymmetric Yang-Mills (SYM) theory. This realization makes manifest their mixing and renormalization properties at one loop. We also extend to the superfield formalism the perturbative and nonperturbative techniques in [1-7] to a large class of supersymmetric theories that are superconformal in the zero-coupling limit. Specifically, we compute the generating functional of superfield twist-$2$ operators in $\mathcal{N}=1$ SU($N$) SYM theory in the zero coupling limit. We also work out in a closed form the corresponding asymptotic renormalization-group improved generating functional in Euclidean superspace and its planar and leading nonplanar large-$N$ expansion. We verify -- as originally predicted in [5] and verified in the component formalism [3, 4, 6, 7] -- that the leading nonplanar asymptotic RG-improved generating functional matches the structure of logarithm of a functional superdeterminant of the corresponding nonperturbative object, which it should be asymptotic to at short distances because of the asymptotic freedom. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SYM theory that may be a pivotal guide for the search of such a solution.

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arXiv2023

Aspects of the Electroweak Skyrmion

We consider certain aspects of the electroweak Skyrmion (EWS). We discuss the case of EWS with dynamical Higgs and find numerical solutions for various values of the cutoff scale. Our results are qualitatively similar to the ones present in the literature, but we find a considerable lower mass than previous studies. We discuss the quantization of the light degrees of freedom and prove that the EWS is a boson. We consider the interaction between fermions and the EWS and the transfer of fermionic charge onto the soliton. We consider the large distance structure of the soliton and the interaction between two well separated EWSs. We find that the classical EWS has a magnetic dipole moment. We discuss the lifetime of the metastable soliton. Finally, we discuss some phenomenological and cosmological consequences of our results.

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