arXiv subjects

Florent Baume

Publications and source records attributed to Florent Baume.

At least 19 recordsLinked to original sources

arXiv2026

Group Theory and the CFT Distance Conjecture: $\mathcal{N}=2$ Tensionless Strings Have No (Co)Weight

We perform a systematic survey of the Hagedorn behaviour at infinite-distance points in the conformal manifold of four-dimensional large-$N$ $\mathcal{N}=2$ Superconformal Field Theories admitting a Lagrangian description. Many properties of these theories can be understood in terms of the Lie algebra encoding the shape of their quiver. We find that in the overall-free limit, the Hagedorn temperature is determined by the largest eigenvalue of an affine or finite Cartan adjacency matrix. This defines two types of universality classes of theories sharing the same high-energy exponential growth of states characteristic of string-like spectra. The first and largest is the affine case, corresponding to orbifold and orientifold projections of $\mathcal{N}=4$ super-Yang-Mills, and all share the same temperature. The others fall into universality classes following an ADE classification with a temperature set by the dual Coxeter number, and can be obtained by deforming the affine case. Our results apply to all large-$N$ $\mathcal{N}=2$ quivers with any classical gauge symmetry, including those with matter charged beyond bifundamental representations. We further discuss the string-theoretic construction of these theories and some of the holographic implications, as well as how our methods extend to broad families of theories with less supersymmetry. We also consider limits where only part of the theory becomes free, and find lower and upper bounds on the exponential rate predicted by the CFT Distance Conjecture. Both these bounds and the Hagedorn temperature are set by the same eigenvalue, and when the quiver has a single gauge node the lower bound is saturated, giving a natural explanation for the three universality classes recently found in the literature.

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arXiv2026

Controlled Chaos in 4D SCFTs

Chaotic dynamics play an important role in a number of physical systems. One of the qualitative hallmarks of this behavior is the appearance of a sufficiently "complex" spectrum of energy levels. This also makes it challenging to directly verify the onset of chaos in interacting quantum field theories. We present a class of 4D superconformal field theories (SCFTs) given by orbifolds of 4D $\mathcal{N} = 4$ Super Yang--Mills theory in which operator mixing in a controlled subsector is described by an effective spin chain in one spatial dimension with nearest neighbor interactions tuned by the marginal couplings of the SCFT. Tuning the marginal couplings results in a chaotic spectrum, while generically the spin chain exhibits Anderson localization. We diagnose the onset of chaos by analyzing the statistical distribution of eigenvalues of the dilatation operator, in particular properties such as eigenvalue level repulsion, spectral rigidity, and the spectral form factor. We also show that other diagnostics such as Krylov complexity sometimes do not faithfully capture this information. This structure defines a chaotic billiard in the target space of the stringy realization. We also comment on the large $N$ holographic dual description, where the controlled single spin chain approximation must be supplemented by multi-trace dynamics, i.e., the splitting and joining of multiple spin chains.

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arXiv2025

The Weight of $Spin(32)/\mathbb{Z}_2$ Little Strings: T-duality and Hasse Diagrams

We study the worldvolume theories of stacks of $Spin(32)/\mathbb{Z}_2$ heterotic NS5-branes probing a transverse singularity $\mathfrak{g}$. We revisit and extend the original classification by Blum and Intriligator, and show that the resulting 6d Little String Theories (LSTs) are naturally labeled by affine dominant coweights of the singularity $\mathfrak{g}$. This in turn enables us to efficiently arrange these theories into groupings satisfying all known necessary conditions to be T-dual. Using this formulation, we then study the partial order of those coweights, and extend a recently proposed slice-subtraction algorithm to construct Hasse diagrams for LSTs directly from their six-dimensional generalized quivers, allowing us to probe certain properties of their Higgs branch. Along the way, we exploit these techniques to show that the number of duality orbits at maximal flavor rank is determined by the center of the transverse singularity $\mathfrak{g}$, and provide a simplified proof of a monotonicity theorem for this class of theories. Finally, we show how some of our techniques can be extended to other classes of 6d theories, such as Type-II LSTs and SCFTs.

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arXiv2024

Constraints on RG Flows from Protected Operators

We consider protected operators with the same conformal dimensions in the ultraviolet and infrared fixed point. We derive a sum rule for the difference between the two-point function coefficient of these operators in the ultraviolet and infrared fixed point which depends on the two-point function of the scalar operator. In even dimensional conformal field theories, scalar operators with exactly integer conformal dimensions are associated with Type-B conformal anomalies. The sum rule, in these cases, computes differences between Type-B anomaly coefficients. We argue the positivity of this difference in cases in which the conformal manifold contains weakly coupled theories. The results are tested in free theories as well as in $\mathcal N = 2$ superconformal QCD, necklace quivers and holographic RG flows. We further derive sum rules for currents and stress tensor two-point functions.

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arXiv2024

The Bestiary of 6d (1,0) SCFTs: Nilpotent Orbits and Anomalies

Many six-dimensional $(1,0)$ SCFTs are known to fall into families labelled by nilpotent orbits of certain simple Lie algebras. For each of the three infinite series of such families, we show that the anomalies for the continuous zero-form global symmetries of a theory labelled by a nilpotent orbit $O$ of $\mathfrak{g}$ can be determined from the anomalies of the theory associated to the trivial nilpotent orbit (the parent theory), together with the data of $O$. In particular, knowledge of the tensor branch field theory is bypassed completely. We show that the known anomalies, previously determined from the geometric/atomic construction, are reproduced by analyzing the Nambu--Goldstone modes inside of the moment map associated to the $\mathfrak{g}$ flavor symmetry of the parent SCFT. This provides further evidence for the physics underlying the labelling of the SCFTs by nilpotent orbits. We remark on some consequences, such as the reinterpretation of the 6d $a$-theorem for such SCFTs in terms of group theory.

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arXiv2024

Bounds and Dualities of Type II Little String Theories

We explore the symmetry structure of Type II Little String Theories and their T-dualities. We construct these theories both from the bottom-up perspective starting with seed Superconformal Field Theories, and from the top-down using F-/M-theory. By exploiting anomaly inflow and unitarity of the LST worldsheet theory, we derive strong conditions on the possible 6D bulk theories and their flavor algebras. These constraints continue to apply if gravity is coupled to the theory. We also study the higher form symmetry structure of these theories and show how they get exchanged under T-duality. Finally, we comment on seemingly consistent bottom-up Little String Theories that cannot be constructed from the top-down approach.

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arXiv2024

SymTrees and Multi-Sector QFTs

The global symmetries of a $D$-dimensional QFT can, in many cases, be captured in terms of a $(D+1)$-dimensional symmetry topological field theory (SymTFT). In this work we construct a $(D+1)$-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly non-topological junctions. In string-realized multi-sector QFTs, these junctions are smoothed out in the extra-dimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$ averaging where the topological sectors of different large $M$ replicas become dressed by additional extended operators associated with the SymTree.

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arXiv2024

On Higher-Spin Points and Infinite Distances in Conformal Manifolds

Distances in the conformal manifold, the space of CFTs related by marginal deformations, can be measured in terms of the Zamolodchikov metric. Part of the CFT Distance Conjecture posits that points in this manifold where part of the spectrum becomes free, called higher-spin points, can only be at infinite distance from the interior. There, an infinite tower of operators become conserved currents, and the conformal symmetry is enhanced to a higher-spin algebra. This proposal was initially motivated by the Swampland Distance Conjecture, one of pillars of the Swampland Program. In this work, we show that the conjecture can be tackled using only methods from the conformal toolkit, and without relying on the existence of a weakly-coupled gravity dual. Via conformal perturbation theory combined with properties of correlators and of the higher-spin algebra, we establish that higher-spin points are indeed at infinite distance in the conformal manifold. We make no assumptions besides the usual properties of local CFTs, such as unitarity and the existence of an energy-momentum tensor. In particular, we do not rely on a specific dimension of spacetime (although we assume $d>2$), nor do we require the presence of supersymmetry.

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arXiv2023

Super-Spin Chains for 6D SCFTs

Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin $s$ Heisenberg spin chain, where $s$ is determined by the $\mathfrak{su}(2)_{R}$ R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra $\mathfrak{osp}(6,2|1)$. In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D $\mathcal{N} = 2$ SCFTs with the same generalized quiver structures.

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arXiv2022

Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus

We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $(\mathfrak{e}_n,\mathfrak{e}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4d SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4d theories from different origins via mirror symmetry.

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arXiv2022

6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains

Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N} = 2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza--Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a $\mathbb{C}^{2}/\mathbb{Z}_{K}$ singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg $XXX_{s=1/2}$ spin chain with open boundary conditions, and similar considerations hold for its $T^2$ reduction to a 4D $\mathcal{N}=2$ SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable $XXX_{s}$ spin chain with $s>1/2$. We also briefly discuss some generalizations to other operator sectors as well as little string theories.

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arXiv2021

Bootstrapping (D, D) Conformal Matter

We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the unitarity bounds for arbitrary $k$. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the anomalous dimensions of low-lying long superconformal multiplets, and find hints for novel OPE selection rules involving type-$\mathcal{B}$ multiplets.

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arXiv2021

Tackling the SDC in AdS with CFTs

We study the Swampland Distance Conjecture for supersymmetric theories with AdS${}_5$ backgrounds and fixed radius through their $\mathcal{N}=2$ SCFT holographic duals. By the Maldacena-Zhiboedov theorem, around a large class of infinite-distance points there must exist a tower of exponentially massless higher-spin fields in the bulk, for which we find bounds on the decay rate in terms of the conformal data. We discuss the origin of this tower in the gravity side for type IIB compactification on $S^5$ and its orbifolds, and comment about more general cases.

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arXiv2020

Instanton Corrections and Emergent Strings

We study limits of infinite distance in the moduli space of 4d $\mathcal{N} = 2$ string compactifications, in which instanton effects dominate. We first consider trajectories in the hypermultiplet moduli space of type IIB Calabi-Yau compactifications. We observe a correspondence between towers of D-brane instantons and D-brane 4d strings, such that the lighter the string the more relevant the instanton effects are. The dominant instantons modify the classical trajectory such that the lightest D-brane string becomes tensionless even faster, while the other strings are prevented to go below the fundamental string tension. This lightest string is dual to a fundamental type IIB string and realises the Emergent String Conjecture. We also consider the vector multiplet moduli space of type I string theory on $K3 \times T^2$ , where quantum corrections can also become significant. Naively, we only find trajectories that correspond to decompactification limits, in apparent contradiction with the picture obtained in some dual setup.

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arXiv2020

Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry

For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data.

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arXiv2017

When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion

We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. To this end we consider complex structure deformations of elliptic fibrations with a Mordell--Weil group of rank one and identify the conditions under which the generating section becomes torsional. For the specific case of Z2 torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU(2) x SU(4)]/Z2 x SU(2). The subsolution with gauge group SU(2)/Z2 x SU(2), for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Z2 torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU(2)/Z2 x Z2 gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.

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arXiv2016

Backreacted Axion Field Ranges in String Theory

String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter is unconstrained by tadpoles and can in principle lead to a parametrically enhanced effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement.

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arXiv2015

The local Callan-Symanzik equation: structure and applications

The local Callan-Symanzik equation describes the response of a quantum field theory to local scale transformations in the presence of background sources. The consistency conditions associated with this anomalous equation imply non-trivial relations among the $β$-function, the anomalous dimensions of composite operators and the short distance singularities of correlators. In this paper we discuss various aspects of the local Callan-Symanzik equation and present new results regarding the structure of its anomaly. We then use the equation to systematically write the n-point correlators involving the trace of the energy-momentum tensor. We use the latter result to give a fully detailed proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also correspond to CFTs. We also clarify the relation between the matrix entering the gradient flow formula for the $β$-function and a manifestly positive metric in coupling space associated with matrix elements of the trace of the energy momentum tensor.

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