iTHEMS-YITP Workshop: Bootstrap, Localization and Holography

May 20, 2024, 9:00 AM → May 24, 2024, 4:00 PM Asia/Tokyo

Panasonic Auditorium, Yukawa Hall (Yukawa Institute for Theoretical Physics, Kyoto University)

Luis Fernando Alday (University of Oxford), Masazumi Honda (RIKEN iTHEMS), Shai M. Chester (Imperial College), YU NAKAYAMA (Yukawa Institute of Theoretical Physics), Yuya Kusuki (California Institute of Technology)

Overview

The primary approach to understanding quantum gravity non-perturbatively is through the AdS/CFT correspondence. The issue is that holographic CFTs are not amenable to traditional perturbative methods. Against this backdrop, two significant non-perturbative techniques have been developed to address this: supersymmetric localization and numerical conformal bootstrap. Recently, it has been shown that the observables computed from localization can be input into the bootstrap to improve bounds, potentially leading to non-perturbative solutions to holographic CFTs, and thus quantum gravity. So far, the bootstrap and localization communities have not overlapped much, due to the high technical barrier of entry to each. This conference aims at overcoming this barrier by bringing together experts from each community.

The conference will include the following topics:

• Numerical conformal bootstrap as applied to holographic CFTs.
• Computation of exact observables using supersymmetric localization.
• Exact relations between correlation functions in CFTs and protected observables amenable to localization.
• Analytic bootstrap methods to compute holographic correlators at large N.
• Questions about quantum gravity that can be answered from future bootstrap results.

---

Speakers

Review talks will be given by

• Joseph Minahan (Uppsala University)

             "Supersymmetric Localization"

• Shai M. Chester (Imperial College)

              "Numerical Bootstrap and Localization"

• Xinan Zhou (Kavli Institute for Theoretical Sciences)

             "Analytic Bootstrap for Holographic Correlators"

Research talks:

• Alessandro Vichi (Pisa University)
• Arthur Lipstein (Durham University)
• Daniele Dorigoni (Durham University)
• Ellis Yuan (Zhejiang University)
• Kazumi Okuyama (Shinshu University)
• Marco Billo (Turin University)
• Maria Nocchi (University of Oxford)
• Ning Su (Caltech)
• Nikolay Gromov (King’s College London)
• Paul Heslop (Durham University)
• Pietro Ferrero (Stony Brook University)
• Ross Dempsey (Princeton University)
• Sanefumi Moriyama (Osaka Metropolitan University)
• Simeon Hellerman (Tokyo University)
• Tobias Hansen (Durham University)
• Tomoki Nosaka (Kavli Institute for Theoretical Sciences)
• Victor Rodriguez (Princeton University)
• Xi Yin (Harvard University)
• Yifan Wang (New York University)

 

---

Registration information

There will be a poster session and we encourage students and young postdocs to present a poster.

The registration deadline is

04/01/2024 (Mon).

If you need a visa, you may need to register early.

---

Acknowledgment

We will be grateful if you acknowledge this workshop in a paper which is initiated or conducted during this workshop. Here are the samples of acknowledgments:

• The authors thank RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program and Yukawa Institute for Theoretical Physics at Kyoto University, where this work was initiated [completed] during "iTHEMS-YITP workshop: Bootstrap, Localization and Holography"  (YITP-W-24-03)  .
• The authors thank RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program and Yukawa Institute for Theoretical Physics at Kyoto University. Discussions during "iTHEMS-YITP workshop: Bootstrap, Localization and Holography" (YITP-W-24-03) were useful in completing this work.
   

---

Organizers

• Luis Fernando Alday (University of Oxford)
• Shai M. Chester (Imperial College)
• Masazumi Honda (RIKEN iTHEMS)
• Yuya Kusuki (Caltech → Kyushu University)
• Yu Nakayama (YITP)

---

Supporting Organizations

This conference is supported by Yukawa Institute for Theoretical Physics, RIKEN iTHEMS, KAKENHI, and JST SAKIGAKE.

Monday, May 20

9:00 AM Registration

1 Review talk on "Analytic Bootstrap for Holographic Correlators"

Speaker: Xinan Zhou (Kavli Institute for Theoretical Sciences)

Kyoto, May 2024.pdf

11:00 AM Coffee break

2 Bootstrapping the AdS Veneziano amplitude

I will present the derivation of the AdS Veneziano amplitude for the scattering of gluons in type IIB string theory on AdS5×S5/Z2​in the presence of D7 branes, in a small curvature expansion. This is achieved by combining a dispersion relation in the dual 4d N=2 SCFT with an ansatz for the amplitude as an open string worldsheet integral over single-valued polylogarithmic functions evaluated on the real line. Single-valued functions arise because curvature corrections can be thought of as extra insertions of soft gravitons. In this way we fix the first two curvature corrections, which satisfy consistency checks in the high energy limit, the low energy expansion as previously fixed using supersymmetric localisation, and for the classical energy of the exchanged massive string operators. Our result predicts new Wilson coefficients and quantum corrections to the energies of massive strings that could be checked with future localisation, semi-classical or integrability computations.

Speaker: Tobias Hansen (Durham University)

12:15 PM Lunch break

3 High energy scattering of strings in AdS

When studying string scattering in flat space, we rely on a world-sheet description, yet extending this to curved backgrounds poses nontrivial challenges. In this talk, we discuss how to compute string amplitudes on AdS as a curvature expansion around flat space and emphasize the pivotal role of single valuedness, akin to its significance in flat space. Specifically, we focus on the AdS Virasoro-Shapiro amplitude and start from its recent representation as a world-sheet integral. We take the next step towards a world-sheet theory in AdS by investigating the high-energy regime. As in flat space, this is accessed by saddle point techniques. Moreover, the path integral representation for the amplitude is dominated by a classical solution. Our algorithm computes AdS classical solutions to arbitrary order in a 1/R expansion, where R is the radius of AdS, in terms of single-valued multiple polylogarithms whose letters are the locations of the punctures. Finally, we show that AdS curvature corrections exponentiate in this limit!

Speaker: Maria Nocchi (University of Oxford)

HE limit - Japan - slides website.pdf

2:45 PM Coffee break

4 A Differential Representation for Holographic Correlators

I will discuss a differential representation for holographic four-point correlators. In this representation, the correlators are given by acting differential operators on certain seed functions. The number of these functions is much smaller than what is normally seen in known examples of holographic correlators, and all of them have simple Mellin amplitudes. This representation establishes a direct connection between correlators in position space and their Mellin space counterparts. The existence of this representation also imposes non-trivial constraints on the structure of holographic correlators. We illustrate these ideas by correlators in AdS5xS5 and AdS5xS3.

Speaker: Ellis Yuan (Zhejiang University)

eyyuan-240520-yitp.pdf

4:15 PM Coffee break

5 Bootstrapping F-theory

We consider a set of 4d N=2 SCFTs defined by N D3 branes probing F-theory singularities with constant value of the axio-dilaton. In these theories we focus on the four-point function of the moment map operator at large N, which is holographically dual to a gluon amplitude in AdS_5 x S^3. We use the relation between a certain integral of the correlator to the mass-deformed sphere free energy of the theory to put constraints on this observable at the first few orders in the 1/N expansion. In the only case admitting a gauge theory description, we can use standard techniques of supersymmetric localization and fix the coefficients of certain higher-derivative terms in the F-theory effective action as functions of the axio-dilaton. On the other hand, the other theories do not have a Lagrangian but we are still able to use their Seiberg-Witten description to fix a logarithmic threshold term in the gluon amplitude, which is regulated by string theory. Our result agrees with the prediction from the flat space limit. This is the first step towards fixing the coefficients of higher-derivative terms in the F-theory effective action using supersymmetric localization, even for strongly coupled fixed points.

Speaker: Pietro Ferrero (Stony Brook University)

2024_05_BootstrappingFtheory_Kyoto.pdf

Tuesday, May 21

6 Doubled Hilbert space in double-scaled SYK

We consider matter correlators in the double-scaled SYK (DSSYK) model. It turns out that matter correlators have a simple expression in terms of the doubled Hilbert space
$\mathcal{H}\otimes\mathcal{H}$, where $\mathcal{H}$ is the Fock space of $q$-deformed oscillator (also known as the chord Hilbert space).
In this formalism, we find that the operator which counts the intersection of chords should be conjugated by certain entangler'' anddisentangler''. We explicitly demonstrate this structure for the two- and four-point functions of matter operators in DSSYK.

Speaker: Kazumi Okuyama (Shinshu University)

okuyama.pdf

10:30 AM Coffee break

7 Double copy and soft limits in (A)dS

The study of the double copy relating gluon to graviton amplitudes and their soft limits has been a major driving force in the study of scattering amplitudes in flat space. I will describe recent progress in generalising these ideas to (A)dS, which may have interesting implications for holography and cosmology.

Speaker: Arthur Lipstein (Durham University)

11:45 AM Lunch break

8 New recursion relation for M2-brane matrix model

In this talk we study a theory of M2-branes with mass deformations. The Fermi gas formalism allows us to calculate all order 1/N corrections to the partition function when mass parameters are small, for which this model is getting attention in various different
contexts such as matrix model and integrable systems, precision holography and conformal bootstrap. Recently, motivated by the connection between the Fermi gas system and topological string (TS/ST correspondence) it was found that the partition function satisfies non-linear difference equations such as q-deformed Painleve/Toda equations. By combining this with the three-dimensional dualities we find a new recursion relation, which is a powerful tool to calculate exact values of the partition function for large but finite N. As an application, we reveal the large N asymptotics of the partition function when the mass parameters are large, where the aforementioned 1/N expansion is invalid due to the instability of 1/N non-perturbative effects interpreted as
M2-instantons in the gravity side.

Speaker: Tomoki Nosaka (Kavli Institute for Theoretical Science)

240519_Kyotobootstrap_Nosaka.pdf

2:30 PM Coffee break

3:00 PM Poster session

6:00 PM Bunquet

Wednesday, May 22

9 Review talk on "Supersymmetric Localization"

Speaker: Joseph Minahan (Uppsala University)

localization_review_kyoto_2024.pdf

10:30 AM Coffee break

10 Remarks about integrated correlators in N=4 and N=2 SYM superconformal theories in d=4

Localization allows to compute via a matrix model integrated forms of correlators, such as a 4-point function or a two-point function in presence of a defect, whose coordinate dependence is not fixed by conformal symmetry. These correlators are interesting as they holographically dual to scattering processes in AdS5 and the integrated results extend the data for a bootstrap reconstruction. In this talk I will focus on two topics. The first one regards the integrated two-point functions in presence of a Wilson line defect in the N=4 theory. Following 2308.16575 (M.B, Frau, Galvagno, Lerda) I will discuss how the Defect CFT constraints and the Ward identities of the preserved supersymmetries determine the measure of integration and I will rephrase their localization computation (already given in 2305.08297) in the so-called ``full Lie algebra'' approach. This technique is well suited for extending the discussion to $N=2$ superconformal theories and my second topic will be the matrix model computation of integrated 4-pt correlators in a specific N=2 superconformal YM theory called E-theory; this part is based on 2311.17178 with Frau, Lerda, Pini.

Speaker: Marco Billo (Turin University)

kyoto-2024.pdf

11:45 AM Lunch break

11 Integrated correlators beyond localisation

I will review 4-pnt half BPS correlators in planar N=4 super Yang-Mills theory (SYM), dual to graviton scattering in AdSxS via AdS/CFT. In particular I will review the generating functions describing them for all charges at both weak and strong coupling. Integrating certain four-point correlators over their space-time dependence yields quantities that can be computed exactly by supersymmetric localisation, whereas correlators with more general charges are not accessible from this method. Nevertheless we propose an exact expression of such integrated correlators, valid for arbitrary 't Hooft coupling. The expression matches with the known exact localisation-based results for specific charges, as well as with all existing perturbative and strong-coupling results in the literature for more general charges. As an application, our result is used to determine certain 7-loop Feynman integral periods and fix previously unknown coefficients in the correlators at strong coupling.

Speaker: Paul Heslop (Durham University)

Kyoto 2024.pdf

2:30 PM Coffee break

12 Scattering from long strings in AdS5 x S5

Motivated by understanding the scattering of gravitons from extended (or long) strings in type IIB string theory at finite coupling via AdS/CFT, we study an integrated two-point function of stress tensor multiplet operators in the presence of a half-BPS line defect in N=4 SU(N) super-Yang-Mills theory.

We determine this integrated correlator at the five lowest non-trivial orders in 1/\sqrt{N} at fixed Yang-Mills coupling and θ-angle. Our calculations are performed explicitly when the line defect is a Wilson line, in which case we find a finite number of perturbative contributions at each order in 1/\sqrt{N}, as well as instanton contributions.

Using SL(2,Z) transformations, our results can also be applied to Wilson-’t Hooft line defects dual to extended (p, q)-strings in the bulk.

We analyze features of these integrated correlators in the weak coupling expansion by comparing with open-closed amplitudes of type IIB string theory on AdS5 x S5, as well as in its flat space limit.

We predict new higher-derivative interaction vertices on the D1-brane and, more generally, on (p, q)-strings.

Speaker: Victor Rodriguez (Princeton University)

4:00 PM Coffee break

13 Modularity and Resurgence for N=4 Integrated Correlators

I will describe a surprisingly simple representation of a class of integrated correlation functions of four superconformal primaries in the stress tensor multiplet of N=4 supersymmetric Yang-Mills theory with arbitrary simple gauge group, G. I then present exact formulae for these integrated correlators which are manifestly invariant under GNO electro-magnetic duality. For classical gauge groups, G=SU(N), SO(N), USp(2N), In the large-N limit these correlators are interpreted via holography in terms of the low-energy expansion of type IIB superstring amplitudes in AdS_5XS^5 or an orientifold thereof.
From the asymptotic perturbative large-N expansion of these integrated correlators we can reconstruct non-perturbative, but modular invariant exponentially suppressed terms via resurgence analysis.

Speaker: Daniele Dorigoni (Durham University)

Thursday, May 23

14 Review talk on "Numerical Bootstrap"

Speaker: Shai Chester (Imperial College)

kyotoReview.pdf

10:30 AM Coffee break

15 Bootstrapping SCFTs with Integral Constraints

The numerical conformal bootstrap has put impressive bounds on the data of CFTs, including superconformal field theories, by using the equations for crossing symmetry of correlators expanded in derivatives of cross-ratios. Supersymmetric localization provides complementary constraints on SCFTs in terms of integrals of correlators over the cross-ratios. In this talk, I will describe how to include these constraints from localization into the bootstrap. I will focus on two examples: 4D N = 4 super-Yang-Mills theory, and 3D ABJM theory. In both cases, the use of integral constraints dramatically improves bootstrap bounds, and enhances the sensitivity of the bounds to higher-derivative corrections coming from the holographic dual models.

Speaker: Ross Dempsey (Princeton University)

Dempsey_Bootstrapping_SCFTS.pdf

11:45 AM Lunch break

16 Tachyon-Dilaton Eschatology and Diffeomorphism in String Field Theory

I will discuss a formulation of conformal perturbation theory through closed string field theory and nontrivial string background deformations described by string fields.

Speaker: Xi Yin (Harvard University)

2:30 PM Coffee break

17 Bootstrapping 3d CFTs with O(N) symmetry

In this talk, I summarize various numerical bootstrap studies on CFTs with O(N) symmetry. These bootstrap problems are translated to very challenging computational tasks, and several advanced numerical techniques have been developed to address the challenges in recent years. I will review these techniques and discuss the O(2), O(3), O(5) studies and the implications for relevant physics questions.

Speaker: Ning Su (Caltech)

4:00 PM Coffee break

18 Spectrum and bootstrap – happy together?

I will review the status of the integrability for the spectrum in N=4 SYM and on how we plan to get beyond the spectrum with the help of the conformal bootstrap.

Speaker: Nikolay Gromov (King’s College London)

2024 Kyoto.pptx

Friday, May 24

19 Global Symmetry and Integral Constraint on Superconformal Impurities

We study properties of point-like impurities preserving flavor symmetry and supersymmetry in four-dimensional N=2 field theories. At large distances, such impurities are described by half-BPS superconformal line defects. By working in the AdS2*S2 conformal frame, we develop a novel, simpler, way of deriving the superconformal Ward identities relating the various two-point functions of flavor current multiplet operators in the presence of the defect. We use these relations to simplify a certain integrated two-point function of flavor current multiplet operators, which is accessible by exact methods such as supersymmetric localization and provides useful input for further bootstrap studies.

Speaker: Yifan Wang (New York University)

defectYITP.pdf

10:00 AM Coffee break

20 1-point blocks for Thermal CFTs

We study conformal blocks for thermal one-point functions on the sphere in the presence of angular potential in conformal field theories. Much like ordinary four-point conformal blocks, the thermal blocks satisfy Dolan-Osborn-like Casimir differential equations. We will obtain a general solution using recursion relations and weight-shifting operators. As an application, we consider the block decomposition for a few examples. We also discuss an asymptotic formula for the three-point coefficients of primary operators in the limit where two of the operators are heavy.

Speaker: Alessandro Vichi (Pisa University)

11:15 AM Coffee break

21 M2-branes, Painleve equations and affine Weyl groups

It was known that multiple M2-branes are described by supersymmetric Chern-Simons theories and the grand canonical partition functions of these theories sometimes satisfy q-deformed Painleve equations. Since Painleve equations are constructed from affine Weyl groups of exceptional algebras, this implies that these grand partition functions enjoy hidden symmetries of affine Weyl groups. After clarifying how symmetries of discrete translations are realized on the grand partition function, we find that the domain of the grand partition function is extended to the whole parameter space of relative ranks, where the q-Painleve equation continues to hold. This work is based on collaborations with Tomoki Nosaka.

Speaker: Sanefumi Moriyama (Osaka Metropolitan University)

12:30 PM Lunch break

22 Bosons and/ or fermions at large charge

In this talk I will review the general semiclassical method of computation of strongly coupled CFT data for operators of large charge Q,
and its application to strongly-coupled bosonic and supersymmetric theories. I will particularly emphasize the use of
double-scaling limits to interpolate continuously between field-theoretic weak-coupling perturbation theory and large-charge EFT,
when a theory-dependent weak-coupling parameter is available. I will then discuss more recent results applying the same
methods to fermionic CFT, including an analysis of a special case (the O(2N) x O(2N)-symmetric Gross-Neveu model) whose large-charge regime is controlled by
Landau Fermi-liquid theory. I will then extend the picture by showing (based on work in progress with Bersini, Orlando and Reffert)
that this theory has a third regime at ultra-large charge described by a novel nonabelian
superfluid phase. I will explain the transition to this phase via the BCS mechanism which is controlled quantitatively by
a second double-scaling limit of Q taken to infinity with Q \exp{-N} held fixed.

Speaker: Simeon Hellerman (Tokyo University)