Spin (8,9,10), Octonions and the Standard Model
Kirill Krasnov University of Nottingham
5509 - 5520 of 20128 Results
Format results
Quantum information and black holes
Johanna Erdmenger University of Würzburg
State sum models with defects
Catherine Meusburger University of Erlangen-Nuremberg
Division algebraic symmetry breaking
Cohl Furey Humboldt University of Berlin
Welcome and Opening Remarks
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Bianca Dittrich Perimeter Institute for Theoretical Physics
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Theo Johnson-Freyd Dalhousie University
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Sylvie Paycha University of Potsdam
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Katarzyna Rejzner University of York
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Anne Taormina Durham University
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Reiko Toriumi Okinawa Institute of Science and Technology Graduate University
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Binary Mergers in Tertiary-induced Channel
Bin Liu University of Waterloo
On the Usefulness of the Strong Exponential Time Hypothesis
Ryan Williams (MIT)Total Function Problems in the Polynomial Hierarchy
Christos Papadimitriou (Columbia University)Structure of SAT Instances
Jordi Levy (Artificial Intelligence Research Institute, Spanish National Research Council), Stefan Szeidar (TU Wien), and Ralf Rothenberger (University of Potsdam)
Spin (8,9,10), Octonions and the Standard Model
Kirill Krasnov University of Nottingham
"I will start by explaining how the (Weyl) spinor representations of the pseudo-orthogonal group Spin(2r+s,s) are the spaces of even and odd polyforms on Cr x Rs. Then, the triality identifies the Majorana-Weyl spinors of Spin(8) with octonions. Combining the two constructions one finds that the groups Spin(8+s,s) all have an octonionic description, with Weyl spinors of this group being a copy of O^(2^s). This also gives an octonionic description of the groups that can be embedded into Spin(8+s,s). Applying this construction to Spin(10,2) gives an octonionic description of Spin(10). The latter arises as the subgroup of Spin(10,2) that commutes with a certain complex structure on the space of its Weyl spinors O4. This gives a description of Weyl spinors of Spin(10) as O2_C, and an explicit description of the Lie algebra of Spin(10) as that of 2x2 matrices (of a special type) with complex (and octonionic) entries. It is well known from the SO(10) GUT that fermions of one generation of the SM can be described as components of a single Weyl spinor of Spin(10). Combining this with the previous construction one gets an explanation of why it is natural to identify elementary particles with components of two copies of complexified octonions. I explicitly describe the dictionary that provides this identification. I also describe how a choice of a unit imaginary octonion induces some natural complex structures on the space of Spin(10) Weyl spinors. For one of these complex structures, its commutant in Spin(10) is SU(2)_L x SU(2)_R x SU(3) x U(1). One thus gets a surprisingly large number of structures seen in the SM from very little input - a choice of a unit imaginary octonion. "Syntax-Guided Program Synthesis
Rajeev Alur (University of Pennsylvania)The classical synthesis problem is to find a program that meets a correctness specification given as a logical formula. Recent work on synthesis and optimization illustrates many potential benefits of allowing the user to supplement the logical specification with a syntactic template that constrains the space of allowed implementations. The formulation of the syntax-guided synthesis problem (SyGuS) is aimed at standardizing the core computational problem common to these proposals in a logical framework. In this talk, we first describe how a wide range of problems such as automatic synthesis of loop invariants, program optimization, program repair to defend against timing-based attacks, and learning programs from examples can be formalized as SyGuS instances. We then explain the counterexample-guided-inductive-synthesis strategy for solving the SyGuS problem, its different instantiations, and experimental evaluation over benchmarks from a variety of applications. As a concrete application of syntax-guided synthesis, we will describe the Sharingan system that uses program synthesis to generate network classification programs at the session layer from positive and negative traffic examples. Sharingan accepts raw network traces as inputs, and reports potential patterns of the target traffic in a domain specific language designed for specifying session-layer quantitative properties. Our experiments show that Sharingan is able to correctly identify patterns from a diverse set of network traces and generates explainable outputs, while achieving accuracy comparable to state-of-the-art learning-based systems. We conclude by discussing challenges and opportunities for future research in syntax-guided program synthesis.Quantum information and black holes
Johanna Erdmenger University of Würzburg
The concepts of quantum information theory play an important role in two seemingly distinct areas of physics: For studying the quantum properties of black holes as well as for devising quantum computing algorithms. Quantum entanglement and computational complexity may be mapped to geometric quantities. This is intimately related to the holographic principle, according to which the information stored in a volume is encoded on its surface, as is the case for black holes. In the talk I will describe the essential new concepts that relate quantum information to geometry and gravity. Technically, this involves generalising quantum information results to quantum field theories, i.e. from finite to infinite-dimensional Hilbert spaces. I will explain how the new relations may be used to obtain both a further understanding of quantum black holes, as well as further advances for the theoretical foundations of quantum computing.State sum models with defects
Catherine Meusburger University of Erlangen-Nuremberg
"We explain how to construct a Turaev-Viro state sum model with defect planes, defect lines and defect points. This is work in progress with John Barrett."Division algebraic symmetry breaking
Cohl Furey Humboldt University of Berlin
Can the 32C-dimensional algebra RCHO offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within RCHO which sets in motion a cascade of breaking symmetries: Spin(10) -> Pati-Salam -> Left-Right symmetric -> Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. It should be noted that this pattern would not have been obvious within the standard formalism.Welcome and Opening Remarks
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Bianca Dittrich Perimeter Institute for Theoretical Physics
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Theo Johnson-Freyd Dalhousie University
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Sylvie Paycha University of Potsdam
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Katarzyna Rejzner University of York
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Anne Taormina Durham University
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Reiko Toriumi Okinawa Institute of Science and Technology Graduate University
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Rational Synthesis
Orna Kupferman (Hebrew U)In the traditional approach to synthesis, the system has to satisfy its specification in all environments. Thus, the components that compose the environment can be seen as if their only objective is to conspire to fail the system. In real life, the components that compose the environment are often entities that have objectives of their own. The approach taken in the field of game theory is to assume that interacting agents are rational, and thus act to achieve their own objectives. Adding rationality to the synthesis setting softens the universal quantification on the environments, and motivates the study of rational synthesis. There, we seek a system that satisfies its specification in all rational environments. The above can be formalized in two different ways. The first is cooperative rational synthesis, where the desired output is a stable profile of strategies to all components in which the objective of the system is satisfied. The second is non-cooperative rational synthesis, where the desired output is a strategy for the system such that its objective is satisfied in every stable profile where she follows this strategy. The talk introduces the two types of rational synthesis and surveys their game-theoretical aspects. In particular, we discuss quantitative rational synthesis and relate cooperative and non-cooperative rational synthesis with the two notions of equilibrium inefficiency in game theory, namely price of stability and price of anarchy. The talk is based on joint work with Shaull Almagor, Dana Fisman, Yoad Lustig, Giuseppe Perelli, and Moshe Y. Vardi.Binary Mergers in Tertiary-induced Channel
Bin Liu University of Waterloo
The detections of gravitational waves (GWs) from merging binary black holes (BHs) have motivated many studies on the dynamical formation of such compact black hole binaries (BHBs). Recent works have suggested that tertiary-induced merger via Lidov–Kozai (LK) oscillations may play a significant role in producing the BHBs detected by the LIGO/VIRGO collaboration. I will talk about the dynamics of merging compact binaries near a rotating supermassive black hole (SMBH) in a hierarchical triple configuration, including various general relativistic (GR) effects. I will show that these GR effects significantly increase the merger fraction of BHBs and produce a wide range of spin orientations when the BHB enters LIGO band. I will also discuss the hierarchical BH mergers in multiple systems, focusing on the constraints on the formation of GW190412, GW190814 and GW190521-like events.
On the Usefulness of the Strong Exponential Time Hypothesis
Ryan Williams (MIT)Over the past 15 years or so, the Strong Exponential Time Hypothesis (SETH) has been very useful for proving conditional hardness for many problems: it's a problem at the heart of fine-grained complexity. In this talk, I will discuss another way in which SETH has been useful.Total Function Problems in the Polynomial Hierarchy
Christos Papadimitriou (Columbia University)The empty pigeonhole principle asserts that, if there are more pigeonholes than pigeons, one pigeonhole must be empty. The corresponding class of total function problems contains all of FNP, and its natural problems include applications of the union bound and several well known explicit constructions. Higher up in the polynomial hierarchy, one finds total function problems related to tournaments and the Sauer-Shelah lemma.Approaches to Scattering in Quantum Gravity and Gauge Theory from Symmetry
Monica Pate Harvard University
The problem of quantum gravity -- i.e. to determine the microscopic structure underlying quantum mechanical theories that reproduce general relativity at long distances -- is a major outstanding problem in modern physics. Solving the quantum gravitational scattering problem is one sharp way to address this question. While in principle effective field theory (EFT) provides a systematic framework for solving scattering problems, in quantum gravity the complete answer requires an infinite number of measurements and thereby fails to predict details of the microscopic structure.
I will present two developments that provide new insight into the gravitational scattering problem. The first is a class of infinite-dimensional symmetries generically found to arise in gauge and gravitational scattering. The infinite number of constraints implied by the symmetries are equivalent to quantum field theoretic soft theorems, which prescribe the pattern of soft radiation produced during a scattering event. The second development is a reformulation of the gravitational scattering problem in which Lorentz symmetry is rendered manifest and realized as the action of the global conformal group in two dimensions. This reformulation, which involves scattering particles of definite boost weight as opposed to energy, offers a new approach precisely because it does not admit the decoupling of low and high-energy physics that underpins the traditional EFT approach. I will describe new perspectives ensuing from these developments on various properties of the gravitational scattering problem, including collinear limits, infrared divergences and universal behavior associated to black hole formation.
Structure of SAT Instances
Jordi Levy (Artificial Intelligence Research Institute, Spanish National Research Council), Stefan Szeidar (TU Wien), and Ralf Rothenberger (University of Potsdam)Topics: Jordi Levy: On the Formal Characterization of Industrial SAT Instances Abstract: Over the last 20 years, SAT solvers have experienced a great improvement in their efficiency when solving practical or industrial SAT problems. This success is surprising, considering that SAT is an NP-complete problem. Over the years, the particular structure of industrial instances has been proposed, informally, as a reason. This has led, for instance, the organizers of the SAT competition to distinguish two tracks, random and industrial, and solvers wining in one track have a poor performance on the other, and vice versa. We think that a better characterization of this structure may be decisive in future improvements of practical SAT solving. During my talk, I'll start revisiting the notions that try to characterize how difficult is to be solved a SAT instance in practice, especially, the notion of "hardness" or tree-like space resolution. I'll discuss some properties that are shared by most industrial SAT instances used in the SAT competition, such as scale-free structure, high modularity, and low fractal dimension, and how these features may influence the performance of practical SAT solvers. I'll finish introducing some models of random SAT instances that try to reproduce these characteristics. Stefan Szeidar: Algorithmic utilization of structure in SAT instances Abstract: In this talk, I will survey various concepts that have been proposed to capture the hidden structure in SAT instances. I will focus on concepts that provide worst-case runtime guarantees for SAT algorithms and discuss a suitable theoretical framework. I will also discuss how these concepts relate to each other and propose questions for further research. Some of the talk's content is covered by the extended and updated Chapter 17, Fixed-Parameter Tractability, of the Handbook of Satisfiability, 2nd edition, 2021. Ralf Rothenberger: Structural Parameters - Heterogeneity and Geometry Abstract: Two characteristic properties seem to be prevalent in the majority of real-world SAT instances, heterogeneous degree distribution and locality. In this talk I present our most recent results trying to understand the impact of these two properties on SAT by studying the resolution proof size of random k-SAT models that allow to control heterogeneity and locality.