Perspectives and Prospects
Hirosi Ooguri
Strings 2022
18 – 22 July

The original title of the session wasViews and Visions, but Rajesh andI thought discussing those would
be above our paygrades and asked
the organizers to tone it down to
Perspectives and Prospects.

In fact, there have been plentyof Views and Visions on string
theory posted on the arXiv overthe past six months.

Snowmass“Snowmass will define the most importantquestions for the field of particle physics andidentify promising opportunities to address them.”
American Physical Society,
Division of Particle Physics Community Planning Exercise

Rather than giving an overview ofthe field by going through these
Snowmass white papers, I would
like to make a few remarks frommy idiosyncratic perspective.

Area
𝑆𝑆 =4𝐺𝐺

“The law that entropy always increases ⎯ thesecond law of thermodynamics – holds, I think,
the supreme position among the laws of Nature.
If someone points out to you that your pet
theory of the universe is in disagreement with
Maxwell’s equations – then so much the worse
for Maxwell’s equations. If it is found to becontradicted by observations – well, theseexperimentalists do bungle things sometimes.
But if your theory is found to be against thesecond law of thermodynamics I can give you
no hope; there is nothing for it but to collapse indeepest humiliation.”
Gifford Lectures delivered by Arthur Eddington
University of Edinburgh, January – March 1927

tram line 71 to
Zentralfriedhof
Gruppe 14 C, #1

Area
𝑆𝑆 =4𝐺𝐺

The black hole entropy formula has inspired
significant progress in string theory andquantum gravity.
Its derivation by Strominger and Vafa gave us
deep insight into microstates of black holes
and led developments of powerful newtechniques.

Area𝑆𝑆 =+ 𝑆𝑆bulk
4𝐺𝐺“better defined than either term on the right hand side”

The 2019 resolution of the puzzle about thevon Neumann entropy of Hawking radiation
demonstrated the power of the quantum
extremal surface formula.
It was a semi-classical calculation, analogous
to the Gibbons-Hawking calculation of theblack hole entropy.
Analogous to the Strominger-Vafa calculation
would be to realize the recent proposal by Akers,
et al. in a theory related to the Einstein gravity.

Wormholes play an important role inthese and other recent developments
such as the study of quantum chaos.
Are the phenomena low dimensional
artifacts or are they suggesting generalfeatures of non-perturbative gravity?
The recent paper by Schlenker andWitten sharpens the puzzle on theirrole in ensemble averaging.

To address the questions on wormholes,• No Global Symmetry• Distance Conjecture• Cobordism Conjecture

Wheeler (1957), …
Vafa, H.O. (2007)
McNamara, Vafa (2019)

may be relevant.
They are closely related to each other,and they seem to be common featuresof all known quantum gravity theories.

An earlier formulation:
After explaining the notion of the natural units,

Autobiographical Notes
by Albert Einstein“…, then only dimensionless constants
could occur in the basic equations ofphysics. Concerning such I would like tostate a theorem which at present cannot
be based upon anything more than upona faith in the simplicity, i.e., intelligibility,of nature: there are no arbitrary
constants of this kind …”

A modern formulation:
Every parameter in quantum gravity is anexpectation value of a dynamical field and canbe varied by changing its expectation value.
Can we prove this statement in AdS/CFT?

Every parameter in quantum gravity is an
expectation value of a dynamical field and canbe varied by changing its expectation value.
If there is a parameter in gravity in AdS, there must
be a corresponding parameter in the dual CFT.
If the CFT parameter can be deformed by adding
an exactly marginal operator to the CFT Lagrangian,
there must be a dynamical field in AdS.

Every parameter in quantum gravity is an
expectation value of a dynamical field and canbe varied by changing its expectation value.
If there is a parameter in gravity in AdS, there must
be a corresponding parameter in the dual CFT.
If the CFT parameter can be deformed by adding
an exactly marginal operator to the CFT Lagrangian,
there must be a dynamical field in AdS.
This conditional clauseis a conjecture in CFT.

Can every CFT parameter 𝜆𝜆 be deformed by adding
an exactly marginal operator 𝜙𝜙 to the CFT Lagrangian?
𝑆𝑆CFT ⟶ 𝑆𝑆CFT + 𝛿𝛿𝛿𝛿 �𝜙𝜙ℝ×ΣThis is analogous to the Noether theorem,
Splittablity: 𝑈𝑈 𝑔𝑔, Σ = ∏𝑖𝑖 𝑈𝑈 𝑔𝑔, Σ𝑖𝑖 when Σ = ⋃𝑖𝑖 Σ𝑖𝑖 ,which was used to proveno global symmetry inquantum gravity. Harlow, H.O.: 1810.05338

Can every CFT parameter 𝜆𝜆 be deformed by adding
an exactly marginal operator 𝜙𝜙 to the CFT Lagrangian?
𝑆𝑆CFT ⟶ 𝑆𝑆CFT + 𝛿𝛿𝛿𝛿 �𝜙𝜙ℝ×ΣThis can be regarded as the Noether theorem fora (−1)-form symmetry.

Can every CFT parameter 𝜆𝜆 be deformed by adding
an exactly marginal operator 𝜙𝜙 to the CFT Lagrangian?
𝑆𝑆CFT ⟶ 𝑆𝑆CFT + 𝛿𝛿𝛿𝛿 �𝜙𝜙ℝ×ΣThis can be regarded as the Noether theorem fora (−1)-form symmetry.

No parameter inquantum gravity⟺

No (−1)-form
global symmetry
in quantum gravity

Snowmass White Paper:
The Analytic Conformal Bootstrap
Hartman, Mazáč, Simmons-Duffin, Zhiboedov“New methods are needed to take advantageof the vast additional data encoded elsewherein the conformal manifold, and to addressquestions about the manifold itself, such aswhether there are universal properties of CFTs
at infinite distance.”

Problem 1: When a unitary CFT has acontinuous parameter, show that there is anexactly marginal operator generating its
deformation.
Problem 2: Find out whether there areuniversal properties of CFTs at infinite
distance in the conformal manifold and, ifso, quantify the properties.

Snowmass Report, Theory Frontier 1 [draft]
Quantum gravity, string theory, and black holes
Conveners: Harlow, Kachru, Maldacena“One question of great experimental and theoreticalinterest is whether quantum gravity can produce
inflationary models with relatively large values of 𝑟𝑟,
the tensor to scalar ratio. … it is possible that there
is a theoretical upper bound for 𝒓𝒓 and it would bevery interesting to understand where it is.”My conversation with the Chair of Caltech’s Division ofPhysics, Mathematics and Astronomy in February 2014:
Chair, “BICEP2 is going to announce that 𝑟𝑟 is 0.2.”
H.O, “Great. It will kill string theory.”
Planck2018

Distance conjecture
allowedregion

Lyth boundScalisi, Valenzuela:
1812.07558

Snowmass White Paper:
Implications of Quantum Gravity for Particle Physics
Draper, Garcia Garcia, Reece“…, we would emphasize that even ‘large-fieldinflation,’ where observable tensor modes could becorrelated with a Planck-scale field space distance,
only requires (to fit cosmological data) thatΔ𝜙𝜙 ~ 𝑂𝑂 1 𝑀𝑀Pl and could be entirely consistent withthis bound.”

A Panorama of Physical Mathematics 2021 [draft]an extended version of the Snowmass white paper on physical mathematics
Bah, Freed, Moore, Nekrasov, Razamat, Schäfer-Nameki“When [the distance conjecture] is mademathematically precise in the context
of Calabi-Yau compactification somevery nontrivial mathematics emerges.”

Finite 𝐺𝐺Newton ⟺ Compact Calabi-Yau

Finite 𝐺𝐺Newton ⟺ Compact Calabi-Yau

There are many important questions on physics andmathematics of compact Calabi-Yau manifolds, andwe need stronger tools to address them.
In topological string theory, for example:

For non-compact Calabi-Yau’s, there are many tools,
such as the topological vertex and matrix models.
For compact Calabi-Yau’s, the BCOV equations
uniquely determine amplitudes up to 𝑔𝑔 ≤ 51
in some of the most favorable cases.

Even in this short story on string theory
from my narrow perspective, concepts froma variety of different areas are connected.
The study of the distance conjecture has been
informed by black holes, wormholes, holography,
conformal field theory, generalized symmetry,bootstrap, physical mathematics, and so on, andmay inform cosmology.

Quantum information
Physical mathematics

A much wider range of topics is discussed in
the cornucopia of Snowmass white papers.
Many-body quantum system

Quantum field theory

Conformal bootstrap
Superconformal field theories

Perturbation theory

Particle physics

Cosmology

Even in this short story on string theory
from my narrow perspective, concepts froma variety of different areas are connected.

For more than 30 years,
the Strings conference series
has been providing a unique
opportunity for us to cometogether as a community,
to hear about the latest
developments on all aspectsof string theory, to exchange
ideas, and to open new
directions of research.

Future ofStrings Conferences

This is not an announcement
to host Strings 2023 at Caltech.

Santa Barbara

Kyoto

Okinawa

Strings Conferences in 1989 – 2022

1989 - 2000

1989 - 2000

2001 – 2010

1989 - 2000

2001 – 20102011 – 2022

Strings Conferences in 1989 – 2022

1/3 : North America
1/3 : Europe
1/3 : Africa, Asia,Brazil, Israel

Invited Scientific Speakers of Strings 2022

Strings
1989 – 2022

Strings 2022
SpeakersIssues to consider• Budget and administrative support.
• Carbon footprint and uses of virtual space.
• Improve the diversity and be welcoming
to all members of our community.
• Support for students and postdocs.
• Access from developing countries.
• Process to select and vet future Strings.
Post your comments at:https://strings2022.zulipchat.com/join/pr2y4ctsdhg7dg3bvgimdz3a/

Sizes of Past Strings Conferences
Strings

Country

Total Expense

Registration

Fundraising#Participants

2021

Brazil2K USD

――2,4802020South Africa

3K USD――2,353

2019

Belgium

335K Euro95K Euro

260K Euro492

2018

Japan

510K USD

60K USD

450K USD

400

2017

Israel260K USD

55K USD

205K USD

301

2016

China

200K USD

50K USD

150K USD

460

2015

India

220K USD

60K USD

160K USD

296

2014

USA

350K USD

132K USD

218K USD

600

2013

South Korea

200K USD

50K USD

150K USD

280

2012

Germany

200K Euro

45K Euro

115K Euro400

From my summary talk at Strings 2021:

Virtual

5 × participants(2 × live participants)
with 1/100 of cost.
Reduce carbon footprints.
On-line discussions
encourage participations ofyoung researchers.
Accessibility.

Real

Chance encounters, smalltalks, and silly questions
often lead to important new
insights and open new
directions of research.
Networking opportunities
for young and not-so-young
researchers.
Comradery.

virtually
Dates to beannounced

String Pheno 2023
3 – 7 July in Daejeon, Korea

String Math 2023

10 – 14 July in Melbourn, Austraria

Acknowledgments

Thank you!
Scientific Committee *Chair: Johanna Erdmenger
Ofer Aharony, Netta Engelhardt,
Jan de Boer, Jerome Gauntlett, Veronika Hubeny,
Andrea Puhm, Suvrat Raju, Sakura Schäfer-Nameki,
Harald Skarke, Julian Sonner, Pedro Vieira* started at Strings 2018 in Okinawa
Gong Show Selection Committee

Nils Carqueville, Laura Donnay, Jan Rosseel,
Harold Steinacker

Thank you!
Anton Rebhan of TU Wien
andfor hosting the public lecture by
Netta Engelhardt:“The Black Hole Information Paradox:
A resolution on the horizon?”
tonight at 7 pm, Festival room of
the Austrian Academy of Sciences

Thank you!
Local Organizing Committee
Veronika Bachleitner, Caslav Brukner, Nils Carqueville,
Stefan Fredenhagen, Olaf Krüger, Max Riegler, Timon Zipfelmaier
Kirill Boguslavski, Laura Donnay, Adrien Fiorucc,
Daniel Grumiller, Andreas Ipp, Ben Koch, Iva Lovrekovic,Rohan Poojary, Anton Rebhan, Romain Ruzziconi,
Harald Skarke, Andrea Smith-Stachowski, Raphaela Wutte
Abhiram Kidambi

Jakob Salzer

Thank you!
Main Organizers

Stefan Fredenhagen

Daniel Grumiller