# LPTENS Summer Institute XLVII

Aug 16 – 25, 2017
LPTENS
Europe/Paris timezone

## Abstracts Summer Institute

Shlomo Razamat (Technion)

The eight field way

We discuss reduction of the E – string theory on a Riemann surface. In particular we identify field theories in four dimensions corresponding to such compactification on arbitrary Riemann surface with arbitrary fluxes for the abelian sub-groups of the E8 flavor symmetry.

Leornardo Rastelli (C.N.Yang Institute for Theoretical Physics)

2d chiral algebras associated to 4d superconformal field theories: review and update

Nadav Drukker (King's College)

Deformations of circular Wilson loop and spectral (in)dependence

Niels Obers (Niels Bohr Institute)

Non-Lorentzian geometry in gravity and string theory

I will present a brief introduction to non-Lorentzian geometries. Subsequently I will present a number of Chern-Simons theories that describe novel non-relativistic theories of gravity in three dimensions along with indications of new types of asymptotic symmetry groups. Finally, I will discuss how non-relativistic geometry plays a role in non-relativistic string theory, including its appearance in tractable limits of the AdS/CFT correspondence.

Kenneth Intriligator (University of California)

Superconformal multiplets and applications

Conformal field theories, and their deformations, provide an avenue to explore the richness of quantum field theory beyond the limited realm of perturbation theory around free fields. Supersymmetry allows for additional insights, including some exact results. This talk will be based on a series of papers done in collaboration with Cordova and Dumitrescu, including some work in progress. We explore and classify the possible multiplets of operators of all possible unitary superconformal field theories above two dimensions, and also their supersymmetry-preserving deformations. The zoo of multiplets contains some oddities, particularly in three and four dimensions. We show that unitary superconformal field theories with more than sixteen supercharges can exist only in three dimensions, and there only as free fields. We find that various possible free-field representations of the conformal group cannot exist in unitary superconformal field theories. We use this to show that mixed gauge / global anomalies cannot occur in SCFTs, though they exist in some non-conformal QFTs. For 6d SCFTs, we find an exact relation between the conformal a-anomaly and ’t Hooft anomalies for the superconformal R-symmetry, and prove that it satisfies the a-theorem for tensor-branch deformations. The absence of mixed anomalies ensures positivity of the a-anomaly for 6d SCFTs built from gauge, hyper, and tensor multiplets. Aspects of Higgs branch deformations of such theories will also be discussed.

Frank Ferrari (Université Libre de Bruxelles)

On the phase diagram of strongly coupled planar matrix quantum mechanics

After a brief general discussion on recent progresses and present line of researches in the field of tensor/SYK models, we shall discuss the remarkable features of the phase diagram of strongly coupled matrix quantum mechanics discovered recently. Most of the talk will be based on 1707.03431.

Albrecht Klemm (Bethe Center for Theoretical Physics, Universität Bonn)

D-brane masses and the motivic Hodge conjecture

We consider the one parameter mirror family W of the quintic in P^4. By mirror symmetry the even Dp-brane masses of the quintic M can be identified with four periods w.r.t to an integral symplectic basis of H_3(W,Z) at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the L-function of the weight four holomorphic Hecke eigenform with eigenvalue one of Gamma_0(25), that was found by Chad Schoen in this context and whose coefficients a_p count the number of solutions of  the mirror quinitic at the conifold over the finite number field F_p as was discovered by del la Ossa, Candelas and Villegas. Using the theory of periods and quasi-periods of Gamma_0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.

Ioannis Papadimitriou (INFN-Trieste & SISSA-Trieste)

Supercurrent anomalies in 4d SCFTs

We use holographic renormalization of minimal N=2 gauged supergravity in order to derive the general form of the quantum Ward identities for 3d N=2 and 4d N=1 superconformal theories on general curved  backgrounds, including an arbitrary fermionic source for the supercurrent. The Ward identities for 4d N=1 theories contain both bosonic and fermionic global anomalies, which we determine explicitly up to quadratic order in the supercurrent source. The Ward identities we derive apply to any superconformal theory, independently of whether it admits a holographic dual, except for the specific values of the a and c anomaly coefficients, which are equal due to our starting point of a two-derivative bulk supergravity theory. We show that the fermionic anomalies lead to an anomalous transformation of the supercurrent under rigid supersymmetry on backgrounds admitting Killing spinors, even if all superconformal anomalies are numerically zero on such backgrounds. The anomalous transformation of the supercurrent under rigid supersymmetry leads to an obstruction to the Q-exactness of the stress tensor in supersymmetric vacua, and may have implications for the applicability of localization techniques. We use this obstruction to the Q-exactness of the stress tensor, together with the Ward identities, in order to determine the general form of the stress tensor and R-current one-point functions in supersymmetric vacua, which allows us to obtain general expressions for the supersymmetric Casimir charges and partition function. The talk is based on arXiv:1703.04299.

Boris Pioline (LPTHE)

Indefinite theta series, black holes and instantons

In type IIB string theory compactified on a Calabi-Yau three-fold, S-duality requires that the sum over D3-D1-D(-1) instantons (with fixed D3-brane charge) must be modular invariant. Correspondingly, in type IIA string theory, holography requires that the D4-D2-D0 black hole partition function (with fixed D4-brane charge) should be modular. In either case, the sum over D1 (resp. D2) charges is given by an indefinite theta series of signature $r(1,b_2-1)$, where $r$ is the D3 (resp. D4) charge. Using physical insight we have found a general way of determining the modular completion of a large class of holomorphic indefinite theta series, generalizing Zweger's method to arbitrary signature. Based on a series of works with Alexandrov, Banerjee and Manschot.

Nikolay Gromov (King's College)

Integrability of conformal fishnet theory

We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N=4 SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the R-matrix of non-compact conformal SU(2,2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N=4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q-functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr(phi_1^J) where phi1 is one of the two scalars of the theory. For J=3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J=3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J=3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2,2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N=4 SYM.

Kyriakos Papadodimas (CERN & University of Groningen)

Aspects of traversable wormholes and the black hole interior