arXiv subjects

Michele Del Zotto

Publications and source records attributed to Michele Del Zotto.

At least 55 records · Page 3Linked to original sources

arXiv2020

Higher Form Symmetries of Argyres-Douglas Theories

We determine the structure of 1-form symmetries for all 4d $\mathcal{N} = 2$ theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities. This is a large class of models, that includes Argyres-Douglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative behaviour of RR fluxes at infinity in the IIB setup. The final result admits a very compact field theoretical reformulation in terms of the BPS quiver. We illustrate our methods in detail in the case of the $(\mathfrak{g}, \mathfrak{g}')$ Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where $\mathcal{N} = 1$ gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such $\mathcal{N} = 1$ Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.

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arXiv2020

Higher Form Symmetries and M-theory

We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d $\mathcal{N}=1$ SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d $\mathcal{N}=1$ SYM theory, where we recover it from a mixed 't Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed 't Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.

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arXiv2020

On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings

We study the spectrum of BPS particles on the Coulomb branch of five-dimensional superconformal field theories (5d SCFTs) compactified on a circle. By engineering these theories in M-theory on ${\mathbf X} \times S^1 $, for ${\mathbf X}$ an isolated Calabi-Yau threefold singularity, we naturally identify the BPS category of the 5d theory on a circle with the derived category of coherent sheaves on a resolution of ${\mathbf X}$. It follows that the BPS spectrum can be studied in terms of 5d BPS quivers, which are the fractional-brane quivers for the singularity ${\mathbf X}$. 5d BPS quivers generalize the well-studied 4d BPS quivers for 4d $\mathcal{N}{=}2$ gauge theories that can be obtained from ${\mathbf X}$ in so-called geometric engineering limits. We study the interplay between 4d and 5d BPS quivers in detail. We particularly focus on examples when ${\mathbf X}$ is a toric singularity, in which case the 5d BPS quiver is given in terms of a brane tiling. For instance, the well-studied $Y^{p,q}$ brane tiling gives a 5d BPS quiver for the $SU(p)_q$ 5d gauge theory. We present a conjecture about the structure of the BPS spectra of a wide class of models, which we test in the simple case of the 5d $SU(2)_0$ theory (more precisely, the $E_1$ SCFT). We also argue that 5d UV dualities can be realized in terms of mutation sequences on the BPS quivers, which are in turn interpreted as autoequivalences of the BPS category.

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arXiv2019

F-theory and the Classification of Little Strings

Little string theories (LSTs) are UV complete non-local 6D theories decoupled from gravity in which there is an intrinsic string scale. In this paper we present a systematic approach to the construction of supersymmetric LSTs via the geometric phases of F-theory. Our central result is that all LSTs with more than one tensor multiplet are obtained by a mild extension of 6D superconformal field theories (SCFTs) in which the theory is supplemented by an additional, non-dynamical tensor multiplet, analogous to adding an affine node to an ADE quiver, resulting in a negative semidefinite Dirac pairing. We also show that all 6D SCFTs naturally embed in an LST. Motivated by physical considerations, we show that in geometries where we can verify the presence of two elliptic fibrations, exchanging the roles of these fibrations amounts to T-duality in the 6D theory compactified on a circle.

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arXiv2019

Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$ fibered over a real line, and the map between the Kähler parameters of $\mathbf{X}$ and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA "reductions" give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity $\mathbf{X}$. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d $\mathcal{N}=1$ gauge theories.

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arXiv2018

Universal Features of BPS Strings in Six-dimensional SCFTs

In theories with extended supersymmetry the protected observables of UV superconformal fixed points are found in a number of contexts to be encoded in the BPS solitons along an IR Coulomb-like phase. For six-dimensional SCFTs such a role is played by the BPS strings on the tensorial Coulomb branch. In this paper we develop a uniform description of the worldsheet theories of a BPS string for rank-one 6d SCFTs. These strings are the basic constituents of the BPS string spectrum of arbitrary rank six-dimensional models, which they generate by forming bound states. Motivated by geometric engineering in F-theory, we describe the worldsheet theories of the BPS strings in terms of topologically twisted 4d $\mathcal{N}=2$ theories in the presence of $1/2$-BPS 2d $(0,4)$ defects. As the superconformal point of a 6d theory with gauge group $G$ is approached, the resulting worldsheet theory flows to an $\mathcal{N}=(0,4)$ NLSM with target the moduli space of one $G$ instanton, together with a nontrivial left moving bundle characterized by the matter content of the six-dimensional model. We compute the anomaly polynomial and central charges of the NLSM, and argue that the 6d flavor symmetry $F$ is realized as a current algebra on the string, whose level we compute. We find evidence that for generic theories the $G$ dependence is captured at the level of the elliptic genus by characters of an affine Kac-Moody algebra at negative level, which we interpret as a subsector of the chiral algebra of the BPS string worldsheet theory. We also find evidence for a spectral flow relating the R-R and NS-R elliptic genera. These properties of the string CFTs lead to constraints on their spectra, which in combination with modularity allow us to determine the elliptic genera of a vast number of string CFTs, leading also to novel results for 6d and 5d instanton partition functions.

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arXiv2018

Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

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arXiv2018

Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds

We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S^3$. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of arXiv:1708.07215, which relates M-theory on TCS $G_2$-manifolds to $E_8\times E_8$ heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the $G_2$-compactification.

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arXiv2017

Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds

We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum $G_2$ manifolds. For a given $G_2$ manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of $G_2$ manifolds, the other is a duality between Type II strings with different chiralities for another pair of mirror manifolds. We clarify the role of the B-field in the construction, and check that the corresponding massless spectra are respected by the generalized mirror maps. We discuss hints towards a homological version based on BPS spectroscopy. We provide several novel examples of smooth, as well as singular, mirror $G_2$ backgrounds via pairs of dual projecting tops. We test our conjectures against a Joyce orbifold example, where we reproduce, using our geometrical methods, the known mirror maps that arise from the SCFT worldsheet perspective. Along the way, we discuss non-Abelian gauge symmetries, and argue for the generation of the Affleck-Harvey-Witten superpotential in the pure SYM case.

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arXiv2017

6D SCFTs and Phases of 5D Theories

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspondence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi--Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kahler cone of the Calabi--Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.

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arXiv2017

On Exceptional Instanton Strings

According to a recent classification of 6d (1,0) theories within F-theory there are only six "pure" 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are $SU(3),SO(8),F_4,E_6,E_7$, and $E_8$. These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For $G$ simply-laced, we determine the 2d $\mathcal{N}=(0,4)$ worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted $S^2$ compactification of the 4d $\mathcal{N}=2$ theories of type $H_2, D_4, E_6, E_7$ and $E_8$ (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding $T^2 \times S^2$ partition functions and the Hilbert series for moduli spaces of $G$ instantons. Such relations allow to bootstrap the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera for a single instanton string are determined. The same method also fixes the elliptic genus for case of one $ F_4 $ instanton. These results unveil a rather surprising relation with the Schur index of the corresponding 4d $\mathcal{N}=2$ models.

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arXiv2017

Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I

It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of giving a better understanding of the above conjecture, in this paper we revisit the description of framed BPS states of four-dimensional relativistic quantum field theories with eight conserved supercharges in terms of supersymmetric quantum mechanics. We unveil aspects of the deep interrelationship in between the Seiberg-dualities of the latter, the discrete symmetries of the theory in the bulk, and quantum discrete integrable systems.

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arXiv2017

Kinetic Mixing at Strong Coupling

A common feature of many string-motivated particle physics models is additional strongly coupled U(1)'s. In such sectors, electric and magnetic states have comparable mass, and integrating out modes also charged under U(1) hypercharge generically yields CP preserving electric kinetic mixing and CP violating magnetic kinetic mixing terms. Even though these extra sectors are strongly coupled, we show that in the limit where the extra sector has approximate N = 2 supersymmetry, we can use formal methods from Seiberg-Witten theory to compute these couplings. We also calculate various quantities of phenomenological interest such as the cross section for scattering between visible sector states and heavy extra sector states, as well as the effects of supersymmetry breaking induced from coupling to the MSSM.

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arXiv2017

Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops

Recently, at least 50 million of novel examples of compact $G_2$ holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry for compactifications of Type II superstrings in this context. We focus on $G_2$ manifolds obtained from building blocks constructed from dual pairs of tops, which are the closest to toric CY hypersurfaces, and formulate the analogue of the Batyrev mirror map for this class of $G_2$ holonomy manifolds, thus obtaining several millions of novel dual superstring backgrounds. In particular, this leads us to conjecture a plethora of novel exact dualities among the corresponding 2d N=1 sigma models.

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arXiv2015

Higher S-dualities and Shephard-Todd groups

Seiberg and Witten have shown that in N=2 SQCD with $N_f=2N_c=4$ the S-duality group PSL(2,Z) acts on the flavor charges, which are weights of Spin(8), by triality. There are other N=2 SCFTs in which SU(2) SYM is coupled to strongly-interacting non-Lagrangian matter: their matter charges are weights of $E_6$, $E_7$ and $E_8$ instead of Spin(8). The S-duality group PSL(2,Z) acts on these weights: what replaces Spin(8) triality for the $E_6,E_7,E_8$ root lattices? In this paper we answer the question. The action on the matter charges of (a finite central extension of) PSL(2,Z) factorizes trough the action of the exceptional Shephard--Todd groups $G_4$ and $G_8$ which should be seen as complex analogs of the usual triality group $\mathfrak{S}_3\simeq \mathrm{Weyl}(A_2)$. Our analysis is based on the identification of S-duality for SU(2) gauge SCFTs with the group of automorphisms of the cluster category of weighted projective lines of tubular type.

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arXiv2015

Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2

We study compactification of 6 dimensional (1,0) theories on T^2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d N=2 geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2,Z) duality symmetry inherited from global diffeomorphisms of the T^2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T^2. Among the resulting 4d N=2 CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class S with punctures from toroidal compactification of (1,0) SCFTs where the curve of the class S theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class S theories with no punctures on arbitrary genus Riemann surface.

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arXiv2015

Galois covers of N=2 BPS spectra and quantum monodromy

The BPS spectrum of many 4d N=2 theories may be seen as the (categorical) Galois cover of the BPS spectrum of a different 4d N=2 model. The Galois group G acts as a physical symmetry of the covering N=2 model. The simplest instance is SU(2) SQCD with N_f=2 quarks, whose BPS spectrum is a Z_2-cover of the BPS spectrum of pure SYM. More generally, N=2 SYM with simply--laced gauge group admits Z_k-covers for all k; e.g. the Z_2-cover of SO(8) SYM is SO(8) SYM coupled to two copies of the E_6 Minahan-Nemeshanski SCFT. Galois covers simplify considerably the computation of the BPS spectrum at G-symmetric points, in both finite and infinite chambers. When the covering and quotient QFTs admit a geometric engineering, say for class S models, the categorical spectral cover may be realized as a covering map in the geometry. A particularly nice instance is when the spectral Galois cover is induced by a modular cover of principal modular curves, X(NM)-> X(M), or, more generally, by regular Grothendieck's dessins d'enfants; the BPS spectra of the corresponding N=2 QFTs have magic properties. The Galois covers allow to study effectively the action of the quantum (half)monodromy of 4d N=2 QFTs. We present several examples and applications of the spectral covering philosophy.

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arXiv2015

On the Defect Group of a 6D SCFT

We use the F-theory realization of 6D superconformal field theories (SCFTs) to study the corresponding spectrum of stringlike, i.e. surface defects. On the tensor branch, all of the stringlike excitations pick up a finite tension, and there is a corresponding lattice of string charges, as well as a dual lattice of charges for the surface defects. The defect group is data intrinsic to the SCFT and measures the surface defect charges which are not screened by dynamical strings. When non-trivial, it indicates that the associated theory has a partition vector rather than a partition function. We compute the defect group for all known 6D SCFTs, and find that it is just the abelianization of the discrete subgroup of U(2) which appears in the classification of 6D SCFTs realized in F-theory. We also explain how the defect group specifies defining data in the compactification of a (1,0) SCFT.

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