**By Yakov Landau**

** ****The Annual Simons Summer Workshop held at the Simons Center for Geometry and Physics is one of the Center’s scientific highlights of the year. In its 15 ^{th} year, this summer’s topic was “Strings and QFT Without SUSY.” However, as one speaker pointed out, this is as broad a subject as non-giraffe biology, and consequentially the Workshop brought together a very diverse group of participants who discussed a wide variety of topics. Over 130 participants from 50 different institutions spent most of their day talking to each other, collaborating on topics as varied as vacuum construction in non SUSY string theory, dualities, bootstrap, and the stability of quantum deSitter space.**

The first week started with the talk by Prof. Hirosi Ooguri (Caltech) entitled *“Symmetry in Quantum Gravity and Other Swampland Conditions.”* He discussed several constraints on low energy phenomena one can infer from consistency of quantum gravity in high energy. Using the AdS/CFT correspondence he showed that there should be no global symmetry and that the charge spectrum should be the maximum allowed. The proof he presented, which does not rely on supersymmetry, generalizes and improves earlier arguments; in particular, it prohibits discrete as well as continuous global symmetry.

In her talk entitled *“Longitudinal String Interactions and Black Hole Dynamics”* Prof. Eva Silverstein (Stanford) discussed quantum corrections to the dynamics of systems containing a Schwarzchild black hole. The model she discussed was one of two strings falling into a black hole at two different times. Silverstein showed how the later string could detect the earlier string. The implications of this may lead to statements about a possible relationship between Hawking radiation leaving the black hole and the matter which fell into a black hole, a relationship which would be impossible classically.

Simons Center’s Prof. Zohar Komargodski gave the first beach talk of the workshop on the topic of *“Dynamics of QCD in Four and Three Dimensions”* in which he worked through cases where the Lagrangian of the theory depended on some parameter not present in the classical theory. He then treated the space of theories as a function of this parameter and used the language of phase transitions to study how the various theories could be smoothly transformed into each other. Komargodski began with Yang-Mills theories and then continued his way into QCD in 3+1 dimensions. By analyzing the domain wall behavior he also showed a duality between 2+1 Chern-Simons matter theories and 3+1 QCD.

Prof. David Lowe (Brown) discussed some of the quantum properties of 4D asymptotically deSitter spacetime in his talk entitled *“Quantum deSitter Spacetime.”* He worked through the effects of finite amounts of energy coming in from infinity in the form of gravitational waves and how this would impact the system as a whole. In particular, Lowe discussed how these perturbations can be dealt with from a quantum perspective. He also touched on various approaches and techniques for holography in this spacetime.

The last talk of the week was given by Prof. Domenico Orlando’s (University of Bern) on *“Accessing the CFT Operator Spectrum at Large Global Charge”* tackled one of the big challenges in quantum field theory – understanding how to deal with strongly coupled systems. Orlando demonstrated a technique for approaching this problem in certain conformal theories in which there is a conserved charge. He showed that in the limit of large charge you can build an effective theory from which the dynamics of the theory can be reconstructed.

Week two started with Prof. Sergei Dubovsky’s (NYU) talk entitled *“TTbar Deformation, NAdS2 Holography and the QCD String,”* where he explained how to use gravitational dressing to obtain a new S-matrix from a given S-matrix for an arbitrary 2D relativistic theory. The new S-matrix is UV complete and exhibits “asymptotic fragility.” He showed that the dressed S-matrix provides the exact solution to the scattering problem in the Jackiw-Teitelboim gravity coupled to the original undressed theory. Dubovsky then showed that the dressing can be obtained as a flat limit of the near AdS holography, and argued that it is equivalent to the TTbar deformation.

Prof. Dalimil Mazac (Perimeter) gave a talk entitled *“Complex-Analytic Conformal Bootstrap”* which he began by discussing the notion of maximal coupling in flat space. He then went on to describe how massive scattering works in large AdS2. He then showed how holography could be used to derive the maximal coupling in AdS2 and that as in flat space, maximal coupling gave rise to Sine-Gordon theory. Finally, he showed how these results could be derived using the analytic conformal bootstrap.

The next beach talk was *“3X”* given by Prof. Sergei Gukov (Caltech). He focused on two related problems, the first being finding techniques for non-Lagrangian QFTs, and the second was to discover how physics can help produce new 4-manifold invariants. One approach to the second problem was based on placing 6d fivebrane theory on a 4-manifold (times a Riemann surface) and studying the effective 2d theory. The Q-cohomology of the latter defines a Vertex Operator Algebra, which appears to be a rather strong invariant of smooth 4-manifolds. Then, he described another, alternative approach, based on topological twists of non-Lagrangian 4D theories. The key element of that approach is a way to present a 4-manifold as a “fibration” of a Riemann surface over a two dimensional disk, called trisection.

Professor Silviu Pufu (Princeton) gave a talk entitled *“AdS _{2}/CFT_{1} From AdS_{4}/CFT_{3}.”* His approach was to start with AdS

_{4}/CFT

_{3}and by using supersymmetric localization on each side of this duality obtain a duality between a weakly coupled AdS

_{2}and an exactly solvable CFT

_{1}, which is not supersymmetric. He finished by showing how the techniques could be generalized and gave examples of dualities which could be derived via localization from other dualities.

The week ended with a talk from Professor Adi Armoni (Swansea) on *“Non Supersymmetric Seiberg Dualities from String Theory.”* He began by reviewing Seiberg dualities in N=1 SQCD. He referred to the N=1 SQCD as an electric theory, and showed how it is dual to a magnetic theory. Using arguments from string theory he then proposed a similar duality without supersymmetry. His gauge theory model is built from two 5-branes connected by a 4-brane and the duality is generated by swapping the 5-branes. He argued for this duality by showing that the anomaly matching criteria is satisfied, a large-N argument, and by using string theory.

The first talk of the third week was by Prof. Simeon Hellerman (Kavli IPMU) on the topic of *“Strongly Coupled Theories At Large Quantum Number.”* He addressed the issue of analyzing strongly coupled theories and looked at several tools for simplifying them. While the usual technique is to modify the theory into a regime where the theory could be better understood, he looked at weakly coupled states of the unmodified theory. He presented this approach by placing it in a pseudo-historical context in line with other large parameter expansions.

There were two shorter talks on Tuesday that week, the first being *“Heterotic and Weakly Coupled: Comments on Non-SUSY Strings for the D-Brane Generation”* by Prof. Keith Dienes (University of Arizona and University of Maryland). He focused on two problems present in non-SUSY strings, finiteness and stability. Using modular invariance, he showed that the folk theorem that the absence of SUSY would give rise to physical tachyons is false. He showed that in the partition function, all the tachyons cancelled out in a fashion which he called “misaligned SUSY.” The most notable feature of this is that they did not cancel out term by term (as they would for SUSY), but rather oscillated in such a way that they only cancelled out in the limit.

The second Tuesday talk was *“A Duality in Quantum Mechanics”* given by Prof. Jaume Gomis (Perimeter). While there are many well studied dualities in quantum field theory, Dr. Gomis presented an example of a duality in quantum mechanics. He worked out a duality between a bosonic particle confined to a ring and a fermionic theory coupled to a background field. He worked through the anomalies in both cases and showed that they were indeed describing the same theory.

Prof. Leonardo Rastelli (YITP) gave the third beach talk, *“The Long-Range Ising Model Revisited: A new Infrared Duality.”* He presented a solution to a 40-year-old problem relating to the second order phase transition in the d-dimensional Ising model. Specifically, he described how the model’s critical exponents depend on a parameter which controls the long range interactions in the theory. There was known to be a certain value of the parameter below which one type of theory would emerge and above which the theory would be different. Rastelli worked out precisely what happens around this special value.

Prof. Igor Klebanov (Princeton) reviewed tensor models in which a novel large N limit is being explored in a talk entitled *“Large N Tensor Models.”* He focused particularly on two types of structures in Feynman diagrams: “snails” and “melons.” He showed how these grow in the large N limit in the vector, matrix and tensor models. He also showed that while in going from vector models to matrix models the theory becomes significantly more complicated, going from matrix to tensor models actually gave rise to useful simplifications because only the diagrams containing “melons” are dominant in the large N limit.

The last talk of the week *“The Eight-Field Way”* was given by Prof. Shlomo Razamat (Technion). He explained how certain “miraculous” properties of superconformal field theories (SCFTs) could be understood in a systematic way. He described a formalism in which we could generate these properties in 4D SCFTs by beginning with a 6D theory and placing it on a Riemann surface. He then showed how the topological properties, and the complex structure of the Riemann surface give rise to the miraculous properties of the resulting 4D SCFT.

The final week began with *“Quantum Teleportation Through Wormholes and the Black Hole Interior”* by Prof. Juan Maldacena (IAS). He discussed how interactions between separated but entangled boundaries of NAdS_{2} allowed wormholes in the interior to become traversable. He showed that this could be seen as the analog of teleportation with ordinary entangled particles. He then showed how the corresponding boundary deformation is analogous to the bosonic degree of freedom in the quantum mechanical SYK model.

Professor Clay Cordova’s (IAS) talk entitled *“Applications of the Average Null Energy Condition”* followed. In classical general relativity the null energy condition ensures many fundamental properties of our spacetime are preserved. Cordova showed that while in quantum gravity the equivalent statement cannot hold, the analog of the average null energy condition can. He demonstrated how this condition places constraints on OPE coefficients and on the scaling dimension in conformal field theories.

The final beach talk was given by Prof. Davide Gaiotto (Perimeter) and attracted intelligent creatures across many species. In addition to the usual participants, a pod of dolphins where obviously interested in *“Topological Field Theory and Gapped Phases of Matter”* and they swam by during the talk. While topological field theories give the low energy description of gapped phases of matter systems, Gaiotto asked whether these in fact give us all the features of these systems. Furthermore, he asked how exactly do we relate mathematical properties of TFTs to physical properties of GPMs. He showed how for some class of GPMs, we can explicitly build a TFT which corresponds to it.

Thursday’s talk was *“Higher-Dimensional Analogs of the Jordan-Wigner Transformation,” *given by Prof. Anton Kapustin (Caltech). The Jordan-Wigner transformation allows one to relate fermionic operators to bosonic ones on a 1-dimensional lattice. He discussed a generalization of this to a correspondence between a fermion system on an n-dimensional lattice and a bosonic system on an n-dimensional lattice with certain symmetry and anomaly constraints. The key idea is that certain bosonic systems have emergent fermions, and that one can reinterpret a physical fermion as a bound state of an emergent fermion with other degrees of freedom.

*“Traversable Wormholes, and Spacetime from Entanglement,”* the final talk of the workshop was given by Professor Daniel Jafferis (Harvard). He discussed some tensions between low energy effective description in the bulk and the exact CFT on the boundary. He showed how entanglement in the boundary CFTs corresponded to a wormhole connecting the two exterior universes. However, if we add an interaction between the CFTs, when looked at on the gravity side, this seemed to make the previously non-traversable wormholes traversable thus connecting the two previously disconnected regions of spacetime.

The talks were held mostly at the Simons Center, except for Wednesdays talks traditionally held at a beach on Fire Island, giving everyone an opportunity to spend time in an environment very different from the normal academic setting. The organizers of the workshop, Prof. Martin Rocek (YITP) and Prof. Cumrun Vafa (Harvard) had the workshop set up so that the talks were not the main focus of the workshop, but served as an appetizer stimulating the conversation. As in years past, we look forward to seeing the wealth of physics this workshop inspires.