arXiv subjects

Kenneth Intriligator

Publications and source records attributed to Kenneth Intriligator.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Families of QFTs

RG flows and IR phases of QFTs can be constrained by generalized symmetries and their anomalies. Broken symmetries act on the space of coupling constants of families of theories, and can also have IR-constraining family anomalies. We generalize family anomaly considerations to cases of broken generalized/categorical symmetries, including higher-group and non-invertible symmetries. We consider the anomaly inflow and SymTFTs of such generalized families of QFTs, and their implications for RG flows and constraints on the IR phases. As examples, we apply family anomalies to study the IR phases of $4d$ QCD-like theories deformed by irrelevant, multi-fermion interactions.

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arXiv2023

Anomalies of 4d $Spin_G$ Theories

We consider 't Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits $Spin_G(4)$ generalized spin structure, with $G$ either gauged or a global symmetry. We discuss methods to directly compute $w_2\cup w_3$ 't Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g. $M_4=\mathbb{CP}^2$. Such anomalies have been discussed for $SU(2)$ gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of ${\cal N}=2$ SYM theory. We directly compute these anomalies for a variety of theories, including general $G$ gauge theories with adjoint fermions, $SU(2)$ gauge theory with fermions in general representations, and $Spin(N)$ gauge theories with fundamental matter. We discuss aspects of matching these and other 't Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for general $G_{\rm gauge}$ theory with $N_f$ adjoint Weyl fermions. For example, in the case of $N_f=2$ we discuss anomaly matching in the IR phase consisting of $h^\vee _{G_{\rm gauge}}$ copies of a $\mathbb{CP}^1$ non-linear sigma model, including for the $w_2w_3$ anomalies when formulated with $Spin_{SU(2)_{\rm global}}(4)$ structure.

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arXiv2022

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics. We review some transformative instances of these novel aspects of symmetry in quantum field theory, and give a broad-brush overview of recent applications.

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arXiv2022

Snowmass White Paper on SCFTs

Superconformal field theories (SCFTs) occupy a central role in the study of many aspects of quantum field theory. In this white paper for the Snowmass process we give a brief overview of aspects of SCFTs in $3\leq D \leq 6$ space-time dimensions, including classification efforts and some of the vast current research trends on the physical and mathematical structures generated by this rich class of physical theories.

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arXiv2020

2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories

We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength $f^{(2)}$, naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current $J^{(2)} \sim * \text{Tr} \left( f^{(2)} \wedge f^{(2)}\right)$. We show that suitable mixed anomalies involving the gauge field $f^{(2)}$ and ordinary 0-form global symmetries, such as flavor or Poincar\'e symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current $J^{(2)}$. We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the 't Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the $a$-type Weyl anomaly of all SCFTs with a tensor branch must be positive, $a > 0$.

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arXiv2019

${\cal N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions

We consider conformal and 't Hooft anomalies in six-dimensional ${\cal N}=(1,0)$ superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and $SU(2)_R$ currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non-supersymmetric CFTs in six dimensions have three independent conformal $c$-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three $c$-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its 't Hooft anomalies. Following earlier work on the conformal $a$-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.

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arXiv2018

Exploring 2-Group Global Symmetries

We analyze four-dimensional quantum field theories with continuous 2-group global symmetries. At the level of their charges such symmetries are identical to a product of continuous flavor or spacetime symmetries with a 1-form global symmetry $U(1)^{(1)}_B$, which arises from a conserved 2-form current $J_B^{(2)}$. Rather, 2-group symmetries are characterized by deformed current algebras, with quantized structure constants, which allow two flavor currents or stress tensors to fuse into $J_B^{(2)}$. This leads to unconventional Ward identities, which constrain the allowed patterns of spontaneous 2-group symmetry breaking and other aspects of the renormalization group flow. If $J_B^{(2)}$ is coupled to a 2-form background gauge field $B^{(2)}$, the 2-group current algebra modifies the behavior of $B^{(2)}$ under background gauge transformations. Its transformation rule takes the same form as in the Green-Schwarz mechanism, but only involves the background gauge or gravity fields that couple to the other 2-group currents. This makes it possible to partially cancel reducible 't Hooft anomalies using Green-Schwarz counterterms for the 2-group background gauge fields. The parts that cannot be cancelled are reinterpreted as mixed, global anomalies involving $U(1)_B^{(1)}$ and receive contributions from topological, as well as massless, degrees of freedom. Theories with 2-group symmetry are constructed by gauging an abelian flavor symmetry with suitable mixed 't Hooft anomalies, which leads to many simple and explicit examples. Some of them have dynamical string excitations that carry $U(1)_B^{(1)}$ charge, and 2-group symmetry determines certain 't Hooft anomalies on the world sheets of these strings. Finally, we point out that holographic theories with 2-group global symmetries have a bulk description in terms of dynamical gauge fields that participate in a conventional Green-Schwarz mechanism.

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arXiv2016

Multiplets of Superconformal Symmetry in Diverse Dimensions

We systematically analyze the operator content of unitary superconformal multiplets in $d > 3$ spacetime dimensions. We present a simple, general, and efficient algorithm that generates all of these multiplets by correctly eliminating possible null states. The algorithm is conjectural, but passes a vast web of consistency checks. We apply it to tabulate a large variety of superconformal multiplets. In particular, we classify and construct all multiplets that contain conserved currents or free fields, which play an important role in superconformal field theories (SCFTs). Some currents that are allowed in conformal field theories cannot be embedded in superconformal multiplets, and hence they are absent in SCFTs. We use the structure of superconformal stress tensor multiplets to show that SCFTs with more than 16 Poincar\'e supercharges cannot arise in $d \geq 4$, even when the corresponding superconformal algebras exist. We also show that such theories do arise in $d = 3$, but are necessarily free.

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arXiv2016

Deformations of $W_{A,D,E}$ SCFTs

We discuss aspects of theories with superpotentials given by Arnold's $A,D,E$ singularities, particularly the novelties that arise when the fields are matrices. We focus on 4d ${\cal N}=1$ variants of susy QCD, with $U(N_c)$ or $SU(N_c)$ gauge group, $N_f$ fundamental flavors, and adjoint matter fields $X$ and $Y$ appearing in $W_{A,D,E}(X,Y)$ superpotentials. Many of our considerations also apply in other possible contexts for matrix-variable $W_{A,D,E}$. The 4d $W_{A,D,E}$ SQCD-type theories RG flow to superconformal field theories, and there are proposed duals in the literature for the $W_{A_k}$, $W_{D_k}$, and $W_{E_7}$ cases. As we review, the $W_{D_\text{even}}$ and $W_{E_7}$ duals rely on a conjectural, quantum truncation of the chiral ring. We explore these issues by considering various deformations of the $W_{A,D,E}$ superpotentials, and the resulting RG flows and IR theories. Rather than finding supporting evidence for the quantum truncation and $W_{D_\text{even}}$ and $W_{E_7}$ duals, we note some challenging evidence to the contrary.

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arXiv2016

Deformations of Superconformal Theories

We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.

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arXiv2015

Supersymmetric asymptotic safety is not guaranteed

It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.

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arXiv2015

Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories

We establish a linear relation between the $a$-type Weyl anomaly and the 't Hooft anomaly coefficients for the $R$-symmetry and gravitational anomalies in six-dimensional $(1,0)$ superconformal field theories. For RG flows onto the tensor branch, where conformal symmetry is spontaneously broken, supersymmetry relates the anomaly mismatch $\Delta a$ to the square of a four-derivative interaction for the dilaton. This establishes the $a$-theorem for all such flows. The four-derivative dilaton interaction is in turn related to the Green-Schwarz-like terms that are needed to match the 't Hooft anomalies on the tensor branch, thus fixing their relation to $\Delta a$. We use our formula to obtain exact expressions for the $a$-anomaly of $N$ small $E_8$ instantons, as well as $N$ M5-branes probing an orbifold singularity, and verify the $a$-theorem for RG flows onto their Higgs branches. We also discuss aspects of supersymmetric RG flows that terminate in scale but not conformally invariant theories with massless gauge fields.

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arXiv2015

Infinitely many N=1 dualities from $m+1-m=1$

We discuss two infinite classes of 4d supersymmetric theories, ${T}_N^{(m)}$ and ${\cal U}_N^{(m)}$, labelled by an arbitrary non-negative integer, $m$. The ${T}_N^{(m)}$ theory arises from the 6d, $A_{N-1}$ type ${\cal N}=(2,0)$ theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree $(m+1, -m)$; the $m=0$ case is the ${\cal N}=2$ supersymmetric $T_N$ theory. The novelty is the negative-degree line bundle. The ${\cal U}_N^{(m)}$ theories likewise arise from the 6d ${\cal N}=(2,0)$ theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) ${T}_N^{(m)}$ theories. The ${T}_N^{(m)}$ and ${\cal U}_N^{(m)}$ theories can be represented, in various duality frames, as quiver gauge theories, built from $T_N$ components via gauging and nilpotent Higgsing. We analyze the RG flow of the ${\cal U}_N^{(m)}$ theories, and find that, for all integer $m>0$, they end up at the same IR SCFT as $SU(N)$ SQCD with $2N$ flavors and quartic superpotential. The ${\cal U}_N^{(m)}$ theories can thus be regarded as an infinite set of UV completions, dual to SQCD with $N_f=2N_c$. The ${\cal U}_N^{(m)}$ duals have different duality frame quiver representations, with $2m+1$ gauge nodes.

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arXiv2014

6d, N=(1,0) Coulomb Branch Anomaly Matching

6d QFTs are constrained by the analog of 't Hooft anomaly matching: all anomalies for global symmetries and metric backgrounds are constants of RG flows, and for all vacua in moduli spaces. We discuss an anomaly matching mechanism for 6d N=(1,0) theories on their Coulomb branch. It is a global symmetry analog of Green-Schwarz-West-Sagnotti anomaly cancellation, and requires the apparent anomaly mismatch to be a perfect square, $\Delta I_8={1\over 2}X_4^2$. Then $\Delta I_8$ is cancelled by making $X_4$ an electric / magnetic source for the tensor multiplet, so background gauge field instantons yield charged strings. This requires the coefficients in $X_4$ to be integrally quantized. We illustrate this for N=(2,0) theories. We also consider the N=(1,0) SCFTs from N small $E_8$ instantons, verifying that the recent result for its anomaly polynomial fits with the anomaly matching mechanism.

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arXiv2014

Matching 3d N=2 Vortices and Monopole Operators

In earlier work with N. Seiberg, we explored connections between monopole operators, the Coulomb branch modulus, and vortices for 3d, N=2 supersymmetric, $U(1)_k$ Chern-Simons matter theories. We here extend the monopole / vortex matching analysis, to theories with general matter electric charges. We verify, for general matter content, that the spin and other quantum numbers of the chiral monopole operators match those of corresponding BPS vortex states, at the top and bottom of the tower associated with quantizing the vortices' Fermion zero modes. There are associated subtleties from non-normalizable Fermi zero modes, which contribute non-trivially to the BPS vortex spectrum and monopole operator matching; a proposed interpretation is further discussed here.

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arXiv2013

Aspects of 3d N=2 Chern-Simons-Matter Theories

We comment on various aspects of the the dynamics of 3d N=2 Chern-Simons gauge theories and their possible phases. Depending on the matter content, real masses and FI parameters, there can be non-compact Higgs or Coulomb branches, compact Higgs or Coulomb branches, and isolated vacua. We compute the Witten index of the theories, and show that it does not change when the system undergoes a phase transition. We study aspects of monopole operators and solitons in these theories, and clarify subtleties in the soliton collective coordinate quantization. We show that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches, with BPS solitons on one branch related to the modulus of the other. Among other results, we show how to derive Aharony duality from Giveon-Kutasov duality.

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arXiv2012

(Delta a) curiosities in some 4d susy RG flows

We explore some curiosities in 4d susy RG flows. One issue is that the compelling candidate a-function, from a-maximization with Lagrange multipliers, has a `strange branch," with reversed RG flow properties, monotonically increasing instead of decreasing. The branch flip to the strange branch occurs where a double-trace deformation Delta W=O ^2 passes through marginality, reminiscent of the condition for the chiral symmetry breaking, out of the conformal window transition in non-susy gauge theories. The second issue arises from Higgsing vevs for IR-free fields, which sometimes superficially violate the a-theorem. The resolution is that some vevs trigger marginal or irrelevant interactions, leading to Delta a=0 and decoupled dilaton on a subspace of the moduli space of vacua. This is contrary to classical intuition about Higgsing. This phenomenon often (but not always) correlates with negative R-charge for the Higgsing chiral operator.

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arXiv2012

Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes

We consider topology changing transitions for M-theory compactifications on Calabi-Yau fourfolds with background G-flux. The local geometry of the transition is generically a genus g curve of conifold singularities, which engineers a 3d gauge theory with four supercharges, near the intersection of Coulomb and Higgs branches. We identify a set of canonical, minimal flux quanta which solve the local quantization condition on G for a given geometry, including new solutions in which the flux is neither of horizontal nor vertical type. A local analysis of the flux superpotential shows that the potential has flat directions for a subset of these fluxes and the topologically different phases can be dynamically connected. For special geometries and background configurations, the local transitions extend to extremal transitions between global fourfold compactifications with flux. By a circle decompactification the M-theory analysis identifies consistent flux configurations in four-dimensional F-theory compactifications and flat directions in the deformation space of branes with bundles.

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