arXiv subjects

Marco Baggio

Publications and source records attributed to Marco Baggio.

15 recordsLinked to original sources

arXiv2019

On $T\bar{T}$ deformations and supersymmetry

We investigate the "$T\bar{T}$" deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $T\bar{T}$ deforming operator can be constructed as a supersymmetric descendant. Here we focus on $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetry. As an example, we analyse in detail the $T\bar{T}$ deformation of a free $\mathcal{N}=(1,0)$ supersymmetric action. We also argue that the link between $T\bar{T}$ and string theory can be extended to superstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the $T\bar{T}$ deformation of a free theory of eight $\mathcal{N}=(1,1)$ scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of $T\bar{T}$ deformations that have recently been discussed in the literature.

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arXiv2018

Strings on NS-NS Backgrounds as Integrable Deformations

We consider the worldsheet S matrix of superstrings on an AdS3xS3xT4 NS-NS background in uniform light-cone gauge. We argue that scattering is given by a CDD factor that is non-trivial only between opposite-chirality particles, yielding a spin-chain-like Bethe Ansatz. Our proposal reproduces the spectrum of non-protected states computed from the Wess-Zumino-Witten description and the perturbative tree-level S matrix. This suggests that the model is an integrable deformation of a free theory similar to those arising from the T-Tbar composite operator.

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arXiv2017

Decoding a Three-Dimensional Conformal Manifold

We study the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional $\mathcal{N}=2$ supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the well-known XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group isomorphic to $S_4$ and can be thought of as an orbifold of $\mathbf{CP}^1$. We use the $4-\varepsilon$ expansion and the numerical conformal bootstrap to calculate the spectrum of conformal dimensions of low-lying operators and their OPE coefficients, and find a very good quantitative agreement between the two approaches.

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arXiv2017

Aspects of Berry phase in QFT

When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing---a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We also argue that a large class of QFTs with rich Berry properties is provided by CFTs with non-trivial conformal manifolds. Using the operator-state correspondence we demonstrate in this case that the Berry connection is equivalent to the connection on the conformal manifold derived previously in conformal perturbation theory. In the special case of chiral primary states in 2d N=(2,2) and 4d N=2 SCFTs the Berry phase is governed by the tt* equations. We present a technically useful rederivation of these equations using quantum mechanics methods.

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arXiv2017

Protected string spectrum in AdS3/CFT2 from worldsheet integrability

We derive the protected closed-string spectra of AdS3/CFT2 dual pairs with 16 supercharges at arbitrary values of the string tension and of the three-form fluxes. These follow immediately from the all-loop Bethe equations for the spectra of the integrable worldsheet theories. Further, representing the underlying integrable systems as spin chains, we find that their dynamics involves length-changing interactions and that protected states correspond to gapless excitations above the Berenstein-Maldacena-Nastase vacuum. In the case of AdS3 x S3 x T4 the degeneracies of such operators precisely match those of the dual CFT2 and the supergravity spectrum. On the other hand, we find that for AdS3 x S3 x S3 x S1 there are fewer protected states than previous supergravity calculations had suggested. In particular, protected states have the same su(2) charge with respect to the two three-spheres.

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arXiv2016

Large-N correlation functions in ${\cal N} = 2$ superconformal QCD

We study extremal correlation functions of chiral primary operators in the large-N SU(N) ${\cal N} = 2$ superconformal QCD theory and present new results based on supersymmetric localization. We discuss extensively the basis-independent data that can be extracted from these correlators using the leading order large-N matrix model free energy given by the four-sphere partition function. Special emphasis is given to single-trace 2- and 3-point functions as well as a new class of observables that are scalars on the conformal manifold. These new observables are particular quadratic combinations of the structure constants of the chiral ring. At weak 't Hooft coupling we present perturbative results that, in principle, can be extended to arbitrarily high order. We obtain closed-form expressions up to the first subleading order. At strong coupling we provide analogous results based on an approximate Wiener-Hopf method.

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arXiv2015

On exact correlation functions in SU(N) ${\cal N} = 2$ superconformal QCD

We consider the exact coupling constant dependence of extremal correlation functions of ${\cal N} = 2$ chiral primary operators in 4d ${\cal N} = 2$ superconformal gauge theories with gauge group SU(N) and N_f=2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt* equations. In the case at hand, the tt* equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equations to a sequence of decoupled semi-infinite Toda chains, similar to the one encountered previously in the special case of SU(2) gauge group. This ansatz requires a surprising new non-renormalization theorem in ${\cal N} = 2$ superconformal field theories. We derive a general 3-loop perturbative formula for 2- and 3-point functions in the ${\cal N} = 2$ chiral ring of the SU(N) theory, and in all explicitly computed examples we find agreement with the tt* equations, as well as the above-mentioned ansatz. This is suggestive evidence for an interesting non-perturbative conjecture about the structure of the ${\cal N} = 2$ chiral ring in this class of theories. We discuss several implications of this conjecture. For example, it implies that the holonomy of the vector bundles of chiral primaries over the superconformal manifold is reducible. It also implies that a specific subset of extremal correlation functions can be computed in the SU(N) theory using information solely from the S^4 partition function of the theory obtained by supersymmetric localization.

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arXiv2015

Higher spins in the symmetric orbifold of K3

The symmetric orbifold of K3 is believed to be the CFT dual of string theory on AdS3 x S3 x K3 at the tensionless point. For the case when the K3 is described by the orbifold T4/Z2, we identify a subsector of the symmetric orbifold theory that is dual to a higher spin theory on AdS3. We analyse how the BPS spectrum of string theory can be described from the higher spin perspective, and determine which single-particle BPS states are accounted for by the perturbative higher spin theory.

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arXiv2014

$tt^*$ equations, localization and exact chiral rings in 4d N=2 SCFTs

We compute exact 2- and 3-point functions of chiral primaries in four-dimensional N=2 superconformal field theories, including all perturbative and instanton contributions. We demonstrate that these correlation functions are nontrivial and satisfy exact differential equations with respect to the coupling constants. These equations are the analogue of the $tt^*$ equations in two dimensions. In the SU(2) N=2 SYM theory coupled to 4 hypermultiplets they take the form of a semi-infinite Toda chain. We provide the complete solution of this chain using input from supersymmetric localization. To test our results we calculate the same correlation functions independently using Feynman diagrams up to 2-loops and we find perfect agreement up to the relevant order. As a spin-off, we perform a 2-loop check of the recent proposal of arXiv:1405.7271 that the logarithm of the sphere partition function in N=2 SCFTs determines the Kähler potential of the Zamolodchikov metric on the conformal manifold. We also present the $tt^*$ equations in general SU(N) N=2 superconformal QCD theories and comment on their structure and implications.

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arXiv2014

Exact correlation functions in SU(2) N=2 superconformal QCD

We report an exact solution of 2- and 3-point functions of chiral primary fields in SU(2) N=2 super-Yang-Mills theory coupled to four hypermultiplets. It is shown that these correlation functions are non-trivial functions of the gauge coupling, obeying differential equations which take the form of the semi-infinite Toda chain. We solve these equations recursively in terms of the Zamolodchikov metric that can be determined exactly from supersymmetric localization on the four-sphere. Our results are verified independently in perturbation theory with a Feynman diagram computation up to 2-loops. This is a short version of a companion paper that contains detailed technical remarks, additional material and aspects of an extension to SU(N) gauge group.

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arXiv2014

Higher Derivative Corrections and Central Charges from Wrapped M5-branes

We compute four-derivative corrections to the AdS supergravity actions arising from the near-horizon geometry of N M5-branes wrapped on either one or two Riemann surfaces. This setup features the novel presence of both gauged isometries as well as nontrivial hypermultiplets. We argue that the 5d Chern-Simons terms receive not only higher-derivative corrections but also contributions from Killing vector parameters, which we find must also be corrected. We check the central charges found by our supergravity methods against the dual field theory results and find perfect agreement at leading and subleading order in N. Along the way, we find higher derivative corrections to general AdS_5 and AdS_3xΣ_g geometries.

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arXiv2012

Conformal Symmetry for Black Holes in Four Dimensions and Irrelevant Deformations

It has been argued several times in the past that the structure of the entropy formula for general non-extremal asymptotically flat black holes in four dimensions can be understood in terms of an underlying conformal symmetry. A recent implementation of this idea, carried out by Cvetič and Larsen, involves the replacement of a conformal factor in the original geometry by an alternative conformal factor in such a way that the near-horizon behavior and thermodynamic properties of the black hole remain unchanged, while only the asymptotics or "environment" of the geometry are modified. The solution thus obtained, dubbed "subtracted geometry", uplifts to an asymptotically AdS$_{3}\times S^{2}$ black hole in five dimensions, and an AdS/CFT interpretation is then possible. Building on this intuition we show that, at least in the static case, the replacement of the conformal factor can be implemented dynamically by means of an interpolating flow which we construct explicitly. Furthermore, we show that this flow can be understood as the effect of irrelevant perturbations from the point of view of the dual two-dimensional CFT, and we identify the quantum numbers of the operators responsible for the flow. This allows us to address quantitatively the validity of CFT computations for these asymptotically flat black holes and provides a framework to systematically compute corrections to the CFT results.

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arXiv2012

Hamilton-Jacobi Renormalization for Lifshitz Spacetime

Just like AdS spacetimes, Lifshitz spacetimes require counterterms in order to make the on-shell value of the bulk action finite. We study these counterterms using the Hamilton-Jacobi method. Rather than imposing boundary conditions from the start, we will derive suitable boundary conditions by requiring that divergences can be canceled using only local counterterms. We will demonstrate in examples that this procedure indeed leads to a finite bulk action while at the same time it determines the asymptotic behavior of the fields. This puts more substance to the belief that Lifshitz spacetimes are dual to well-behaved field theories. As a byproduct, we will find the analogue of the conformal anomaly for Lifshitz spacetimes.

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arXiv2012

Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model

In this note we investigate the anomalous breaking of anisotropic scaling symmetry in a non-relativistic field theory with dynamical exponent z=2. On general grounds, one can show that there exist two possible "central charges" which characterize the breaking of scale invariance. Using heat kernel methods, we compute these two central charges in the quantum Lifshitz model, a free field theory which is second order in time and fourth order in spatial derivatives. We find that one of the two central charges vanishes. Interestingly, this is also true for strongly coupled non-relativistic field theories with a geometric dual described by a metric and a massive vector field.

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arXiv2012

A non-renormalization theorem for chiral primary 3-point functions

In this note we prove a non-renormalization theorem for the 3-point functions of 1/2 BPS primaries in the four-dimensional N = 4 SYM and chiral primaries in two dimensional N =(4,4) SCFTs. Our proof is rather elementary: it is based on Ward identities and the structure of the short multiplets of the superconformal algebra and it does not rely on superspace techniques. We also discuss some possible generalizations to less supersymmetric multiplets.

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