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Elli Pomoni

Publications and source records attributed to Elli Pomoni.

At least 37 records · Page 2Linked to original sources
arXiv2021

Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs

This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $\mathcal{N}=2$ SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the $R$-matrix read off from the superpotential. This implies that when orbifolding the $\mathcal{N}=4$ symmetry algebra down to the $\mathcal{N}=2$ one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. Concretely, for the $\mathbb{Z}_2$ quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. We confirm our analytic results by numerical comparison with the explicit diagonalisation of the Hamiltonian for short closed chains.

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arXiv2021

The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class $\mathcal{S}_k$

Even though for generic $\mathcal{N}=1$ theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of $\mathcal{N}=1$ SCFTs, these of Class $\mathcal{S}_k$ for which it is possible to define Coulomb and Higgs branches precisely as for the $\mathcal{N}=2$ theories of Class $\mathcal{S}$ from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional $(1,1)$ Little String theory can be deconstructed from a toroidal quiver in class $\mathcal{S}_k$

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arXiv2020

4d $\mathcal{N}=3$ indices via discrete gauging

A class of 4d $\mathcal{N}=3$ SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of $\mathcal{N}=4$ Super Yang-Mills theory. This discrete subgroup contains elements of both the $SU(4)$ R-symmetry group and the $SL(2,\mathbb{Z})$ S-duality group of $\mathcal{N}=4$ SYM. We give a prescription for how to perform the discrete gauging at the level of the superconformal index and Higgs branch Hilbert series. We interpret and match the information encoded in these indices to known results for rank one $\mathcal{N}=3$ theories. Our prescription is easily generalised for the Coloumb branch and the Higgs branch indices of higher rank theories, allowing us to make new predictions for these theories. Most strikingly we find that the Coulomb branches of higher rank theories are generically not-freely generated.

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arXiv2020

From quantum curves to topological string partition functions

This paper describes the reconstruction of the topological string partition function for certain local Calabi-Yau (CY) manifolds from the quantum curve, an ordinary differential equation obtained by quantising their defining equations. Quantum curves are characterised as solutions to a Riemann-Hilbert problem. The isomonodromic tau-functions associated to these Riemann-Hilbert problems admit a family of natural normalisations labelled by the chambers in the extended Kähler moduli space of the local CY under consideration. The corresponding isomonodromic tau-functions admit a series expansion of generalised theta series type from which one can extract the topological string partition functions for each chamber.

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arXiv2019

4D $\mathcal{N}=2$ SCFTs and spin chains

This is the writeup of the lectures given at the Winter School "YRISW 2018" to appear in a special issue of JPhysA. In the first part of these lecture notes we review some important facts about 4D $\mathcal{N}=2$ SCFTs. We begin with basic textbook material, the supersymmetry algebra and its massless representations and the construction of Lagrangians using superspace. Then we turn to more modern topics, the study of the $\mathcal{N}=2$ SCA and its representation theory. Our intention is to understand how much we can learn from representation theory alone, even about the dynamics of $\mathcal{N}=2$ SCFTs. In the second part of the notes we use these tools to construct spin chains for $\mathcal{N}=2$ SCFTs, the spectral problem of which computes anomalous dimensions of local operators. We discuss their novel features comparing them with their counterparts in $\mathcal{N}=4$ SYM and search for possible integrability structures that emerge.

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arXiv2019

Trinion Conformal Blocks from Topological strings

In this paper we investigate the relation between conformal blocks of Liouville CFT and the topological string partition functions of the rank one trinion theory $T_2$. The partition functions exhibit jumps when passing from one chamber in the parameter space to another. Such jumps can be attributed to a change of the integration contour in the free field representation of Liouville conformal blocks. We compare the partition functions of the $T_2$ theories representing trifundamental half hypermultiplets in $N=2$, $d=4$ field theories to the partition functions associated to bifundamental hypermultiplets. We find that both are related to the same Liouville conformal blocks up to inessential factors. In order to establish this picture we combine and compare results obtained using topological vertex techniques, matrix models and topological recursion. We furthermore check that the partition functions obtained by gluing two $T_2$ vertices can be represented in terms of a four point Liouville conformal block. Our results indicate that the $T_2$ vertex offers a useful starting point for developing an analog of the instanton calculus for SUSY gauge theories with trifundamental hypermultiplets.

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arXiv2018

Toda conformal blocks, quantum groups, and flat connections

This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the $\mathcal{W}$-algebras to define natural bases for spaces of conformal blocks of the Toda conformal field theory associated to the Lie algebra ${\mathfrak s}{\mathfrak l}_3$ on the three-punctured sphere with representations of generic type associated to the three punctures. The operator-valued monodromies of degenerate fields can be used to describe the quantisation of the moduli spaces of flat $\mathrm{SL}(3)$-connections. It is shown that the matrix elements of the monodromies can be expressed as Laurent polynomials of more elementary operators which have a simple definition in the free field representation. These operators are identified as quantised counterparts of natural higher rank analogs of the Fenchel-Nielsen coordinates from Teichmüller theory. Possible applications to the study of the non-Lagrangian SUSY field theories are briefly outlined.

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arXiv2017

Instanton counting in Class $\mathcal{S}_k$

We compute the instanton partition functions of $\mathcal{N}=1$ SCFTs in class $\mathcal{S}_k$. We obtain this result via orbifolding Dp/D(p-4) brane systems and calculating the partition function of the supersymmetric gauge theory on the worldvolume of $K$ D(p-4) branes. Starting with D5/D1 setups probing a $\mathbb{Z}_\ell\times \mathbb{Z}_k$ orbifold singularity we obtain the $K$ instanton partition functions of 6d $(1,0)$ theories on $\mathbb{R}^4 \times T^2$ in the presence of orbifold defects on $T^2$ via computing the 2d superconformal index of the worldvolume theory on $K$ D1 branes wrapping the $T^2$. We then reduce our results to the 5d and to the 4d instanton partition functions. For $k=1$ we check that we reproduce the known elliptic, trigonometric and rational Nekrasov partition functions. Finally, we show that the instanton partition functions of $SU(N)$ quivers in class $\mathcal{S}_k$ can be obtained from the class $\mathcal{S}$ mother theory partition functions with $SU(kN)$ gauge factors via imposing the `orbifold condition' $a_{\mathcal{A}} \rightarrow a_A e^{2πi j/k}$ with $\mathcal{A}=jA$ and $A=1,\dots, N$, $j=1,\dots, k$ on the Coulomb moduli and the mass parameters.

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arXiv2017

Exact Deconstruction of the 6D (2,0) Theory

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the $A$-type (2,0) theories on $T^2$, starting from a four-dimensional $\mathcal N=2$ circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D $\mathcal N=2$ quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on $S^4$ to the (2,0) partition function on $S^4 \times T^2$. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

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arXiv2017

2D CFT blocks for the 4D class $\mathcal{S}_k$ theories

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N} = 1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the $\mathcal{N} = 1$ gauge theories. We find that the blocks corresponding to the SU(N) $\mathcal{S}_k$ gauge theories involve fields in certain non-unitary representations of the $W_{kN}$ algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D $\mathcal{N} = 1$ SCFTs of class $\mathcal{S}_k$.

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arXiv2016

Toda 3-Point Functions From Topological Strings II

In arXiv:1409.6313 we proposed a formula for the 3-point structure constants of Toda field theory, derived using topological strings and the AGT-W correspondence from the partition functions of the non-Lagrangian $T_N$ theories on $S^4$. In this article, we show how the semi-degeneration of one of the three primary fields on the Toda side corresponds to a particular Higgsing of the $T_N$ theories and derive the well-known formula by Fateev and Litvinov.

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arXiv2016

Exact Bremsstrahlung and Effective Couplings

We calculate supersymmetric Wilson loops on the ellipsoid for a large class of $\mathcal{N}=2$ SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the $\mathcal{N}=4$ SYM ones, we obtain interpolating functions $f(g^2)$ such that a given $\mathcal{N}=2$ SCFT observable is obtained by replacing in the corresponding $\mathcal{N}=4$ SYM result the coupling constant by $f(g^2)$. These "exact effective couplings" encode the finite, relative renormalization between the $\mathcal{N}=2$ and the $\mathcal{N}=4$ gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.

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arXiv2014

Fiber-Base Duality and Global Symmetry Enhancement

We show that the 5D Nekrasov partition functions enjoy the enhanced global symmetry of the UV fixed point. The fiber-base duality is responsible for the global symmetry enhancement. For $SU(2)$ with $N_f\leq 7$ flavors the fiber-base symmetry together with the manifest flavor $SO(2N_f)$ symmetry generate the $E_{N_f+1}$ global symmetry, while in the higher rank case the manifest global symmetry of the two dual theories related by the fiber-base duality map generate the symmetry enhancement. The symmetry enhancement at the level of the partition function is manifest once we chose an appropriate reparametrization for the Coulomb moduli.

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arXiv2014

Toda 3-Point Functions From Topological Strings

We consider the long-standing problem of obtaining the 3-point functions of Toda CFT. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. In arXiv:1310.3841 we computed the partition function of 5D $T_N$ theories on $S^4 \times S^1$ and suggested that they should be interpreted as the three-point structure constants of q-deformed Toda. In this paper, we provide the exact AGT-W dictionary for this relation and rewrite the 5D $T_N$ partition function in a form that makes taking the 4D limit possible. Thus, we obtain a prescription for the computation of the partition function of the 4D $T_N$ theories on $S^4$, or equivalently the undeformed 3-point Toda structure constants. Our formula, has the correct symmetry properties, the zeros that it should and, for $N=2$, gives the known answer for Liouville CFT.

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arXiv2014

Integrability in N=2 superconformal gauge theories

Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1|2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1|2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.

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arXiv2014

The Exact Effective Couplings of 4D N=2 gauge theories

The anomalous dimensions of operators in the purely gluonic SU(2,1|2) sector of any planar conformal N=2 theory can be read off from the N=4 SYM results by replacing the N=4 coupling constant by an interpolating function of the N=2 coupling constants, to which we refer to as the effective coupling. For a large class of N=2 theories we compute the weak coupling expansion of these functions as well as the leading strong coupling term by employing supersymmetric localization. Via Feynman diagrams, we interpret our results as the relative (between N=2 and N=4) finite renormalization of the coupling constant. Using the AdS/CFT dictionary, we identify the effective couplings with the effective string tensions of the corresponding gravity dual theories. Thus, any observable in the SU(2,1|2) sector can be obtained from its N=4 counterpart by replacing the N=4 coupling constant by the universal, for a given theory, effective coupling.

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arXiv2013

Non-Lagrangian Theories from Brane Junctions

In this article we use 5-brane junctions to study the 5D T_N SCFTs corresponding to the 5D N=1 uplift of the 4D N=2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n-point functions of the q-deformed W_N Toda theories.

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