Review
Physics, Multidisciplinary
Shai M. Chester
Summary: These lectures aim to familiarize students with the nuts and bolts of numerical bootstrap in an efficient manner, covering the basics of conformal field theory, computation of conformal blocks, formulation of crossing equations as a semi-definite programming problem, solving the problem using SDPB, and interpretation of the results. The lectures include worked examples and problem sets to help students master the skills, culminating in a precise computation of the critical exponents of the 3d Ising model.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2023)
Article
Astronomy & Astrophysics
Cristobal Laporte, Nora Locht, Antonio D. Pereira, Frank Saueressig
Summary: Wetterich's equation is a powerful tool for studying the existence and universality of renormalization group fixed points with quantum scale invariance. A new approximation scheme is developed by projecting the functional renormalization group equation onto functions of the kinetic term. This projection reveals a new universality class with a unique spectrum of stability coefficients for scalars and gauge fields. The implications of these findings for asymptotically safe gravity-matter systems are discussed.
Review
Physics, Multidisciplinary
Henriette Elvang
Summary: This article introduces two highly active research programs, conformal Bootstrap and scattering amplitudes, focusing on the common ideas and methods shared by these two programs, and exploring the possibility of consistent quantum field theories.
REPORTS ON PROGRESS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Matan Lotem, Eran Sela, Moshe Goldstein
Summary: In this study, the researchers extend the Wilson's numerical renormalization group (NRG) method to investigate the system of two Kondo impurities coupled at different locations through unidirectional channels. The results show that, despite the restriction of the mediated interimpurity interactions by the unidirectional channels, the local properties and thermodynamic quantities remain unaffected.
Article
Physics, Multidisciplinary
Yijian Zou, Shengqi Sang, Timothy H. Hsieh
Summary: We analyze the effect of decoherence, modeled by local quantum channels, on quantum critical states and find universal properties of entanglement in resulting mixed states. We define a renormalization group flow between quantum channels and relate the subleading logarithmic scaling of subsystem entropy to correlation functions in conformal field theory. We also show that the subsystem entanglement negativity can exhibit different scaling behaviors based on the renormalization group flow. Our results are important for understanding quantum critical states in noisy quantum simulators.
PHYSICAL REVIEW LETTERS
(2023)
Review
Physics, Multidisciplinary
Claudio Coriano, Matteo Maria Maglio
Summary: This article provides an overview of conformal field theories in coordinate space, focusing on the solution of conformal constraints for three- and four-point functions in momentum space. The study discusses the characteristics of correlators containing stress-energy tensors, conserved currents, and scalar operators, along with anomalies and dual conformal solutions identified by CWIs. Perturbative realizations of CFTs at one-loop are also explored, offering insights into the general solutions identified by CWIs for various operators.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2022)
Article
Computer Science, Interdisciplinary Applications
D. X. Horvth, K. Hdsgi, G. Takcs
Summary: The Truncated Conformal Space Approach (TCSA) is an efficient method for computing spectra, operator matrix elements, and time evolution in quantum field theories. The Chirally Factorised TCSA (CFTCSA) algorithm improves the truncation level and allows for more precise calculations and larger Hilbert space dimensions.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Mechanics
Gavin Rockwood
Summary: The N interval replicated negativity for the Ising conformal field theory is calculated using correlation functions of branch point twist fields, leading to formulas that align with known results.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Materials Science, Multidisciplinary
Guangjie Li, Elio J. Koenig, Jukka I. Vayrynen
Summary: This study proposes a mesoscopic setup for the Kondo effect that can produce emergent anyons, including Majorana fermions, Fibonacci anyons, and Z3 parafermions, even without perfect channel symmetry. The model is mapped to the multichannel Kondo effect associated with an internal SU(2) symmetry, and the scaling of various observables, including conductance, is predicted using conformal field theory. This work not only provides a platform for robust Kondo-based anyons, but also sheds light on the physics of strongly correlated materials with competing order parameters.
Article
Physics, Multidisciplinary
Guangjie Li, Yuval Oreg, Jukka I. Vaeyrynen
Summary: A Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity spin transforms under the orthogonal group SO(M). The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated N-channel generalization of the topological Kondo model.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Multidisciplinary
Donghoon Kim, Jeongmin Shim, H-S Sim
Summary: The study focuses on computing entanglement in spin-1/2 impurity problems and investigates the thermal decay of entanglement in multichannel Kondo effects. Results show that entanglement reaches a maximal value at zero temperature and exhibits a power-law thermal decay at low temperatures, with the power-law exponent being linked to the scaling dimension of the BCFT boundary operator. These findings align with numerical renormalization group results, shedding light on quantum coherence within the Kondo screening length.
PHYSICAL REVIEW LETTERS
(2021)
Review
Physics, Multidisciplinary
Luis Alvarez-Gaume, Domenico Orlando, Susanne Reffert
Summary: This review explores quantum field theories and conformal field theories with global symmetries in the large charge limit, revealing that at low energies, the sectors with large charge can be described using a hybrid form of Goldstone's theorem. The associated effective field theory in the infrared enables computation of anomalous dimensions and operator product expansion coefficients, offering a well-defined expansion in inverse powers of the global charge.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2021)
Article
Physics, Multidisciplinary
O. Lisovyy, A. Naidiuk
Summary: The connection formulas between the Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed using the large order asymptotics of the corresponding power series. It is demonstrated that for various types of Heun equations, the series expansion of the relevant asymptotic amplitude can be computed systematically to any order, allowing for the verification of a recent conjecture relating to the Heun connection matrix.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Simone Giombi, Himanshu Khanchandani, Xinan Zhou
Summary: In this study, conformal field theories on the real projective space RPd were analyzed, focusing on the two-point functions of scalar operators. Based on calculations of Witten diagrams on the quotient space AdS(d+1)/Z(2), an analytic approach to two-point functions was developed by converting the structure of conformal block decomposition into specific sum rules.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Review
Physics, Multidisciplinary
Agnese Bissi, Aninda Sinha, Xinan Zhou
Summary: This review provides a pedagogical introduction to the analytic conformal bootstrap program and reviews analytic methods and explicit examples related to it.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2022)
Article
Physics, Mathematical
Chang-Tse Hsieh, Yuji Tachikawa, Kazuya Yonekura
Summary: The focus of this study is on the gravitational and Green-Schwarz type anomalies of chiral and non-chiral p-form gauge fields. These anomalies naturally arise as boundary modes of higher-dimensional bulk topological phases. By computing the Atiyah-Patodi-Singer eta-invariant, we provide a systematic description of the total bulk-boundary system, analogous to the realization of a chiral fermion on the boundary of a massive fermion. The SL(2, Z) anomaly of the 4D Maxwell theory is determined using our formalism, and we also investigate the worldvolume theories of D-branes and M5-branes in different string, M, and F theories.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Mathematical
Tzu-Chen Huang, Ying-Hsuan Lin
Summary: We construct a topological field theory that realizes the transparent Haagerup H-3 fusion category through its topological defect lines. This theory has six vacua and a total of 15 point-like operators. By solving equations, we determine the TFT data and verify the representation of Cardy states under TDL fusion. The construction of TFTs with two or four vacua remains open. Additionally, gauging algebra objects allows us to obtain TFTs realizing the Haagerup H-1 and H-2 fusion categories.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Justin Kaidi, Kantaro Ohmori, Yunqin Zheng
Summary: We introduce a class of noninvertible topological defects in (3 + 1)D gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)D critical Ising model. Examples include SO(3) Yang-Mills (YM) at theta = pi, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at tau = i. We also introduce an analogous construction in (2 + 1)D, and give a number of examples in Chern-Simons matter theories.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Particles & Fields
Yichul Choi, Kantaro Ohmori
Summary: This study investigates parameterized invertible field theories using the Atiyah-Patodi-Singer index theorem, focusing on the case of free Dirac fermions with spacetime-dependent mass parameters.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Mathematical
Takumi Ichikawa, Yuji Tachikawa
Summary: We study the super version of the Frobenius-Schur indicator in the case when a homomorphism ? : G -> Z/2Z gives the group algebra C[G] the structure of a superalgebra. This indicator distinguishes among the eight types of irreducible real super representations described in Wall (in J Reine Angew Math 213:187-199, 1963/64). Its significance is also discussed in the context of two-dimensional finite-group gauge theories on pin(-) surfaces.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Particles & Fields
Benjamin Assel, Yuji Tachikawa, Alessandro Tomasiello
Summary: We introduce a class of 3d theories consisting of strongly-coupled N = 4 systems coupled to N = 3 Chern-Simons gauge multiplets, which exhibit N = 4 enhancements when a peculiar condition on the Chern-Simons levels is met. We also show that some but not all of these N = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of N = 4 theories which have not been studied previously.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Ying-Hsuan Lin, Masaki Okada, Sahand Seifnashri, Yuji Tachikawa
Summary: This paper investigates the case of a 2d CFT in a fusion category C, where the asymptotic density of states is proportional to (dim ρ)^2 for an irreducible representation ρ of a finite symmetry group G, even when the symmetry can be non-invertible.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Correction
Physics, Mathematical
Yuji Tachikawa, Mayuko Yamashita
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Mathematical
Yuji Tachikawa, Mayuko Yamashita
Summary: In this paper, we mathematically reformulate the question of the absence of global anomalies in heterotic string theory using the Segal-Stolz-Teichner conjecture. By studying the natural transformation between topological modular forms and the Anderson dual of string bordism groups, we prove that this transformation always vanishes, thus indicating the absence of heterotic global anomalies. The importance of TMF21(pt) = 0 in this process is also discussed, along with the description of TMF twists under the Segal-Stolz-Teichner conjecture using the results of Freed and Hopkins on anomalies of quantum field theories. Additionally, separate introductions are provided for mathematicians and string theorists to make the content more accessible, with clear demarcation between mathematically rigorous and non-rigorous sections.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Masaki Tezuka, Onur Oktay, Enrico Rinaldi, Masanori Hanada, Franco Nori
Summary: The sparse version of the Sachdev-Ye-Kitaev model reduces the number of disorder parameters while reproducing essential features of the original model. In this Research Letter, a further simplification called the binary-coupling sparse SYK model is proposed. This model sets the nonzero couplings to be +/- 1 instead of sampling from a continuous distribution. Remarkably, this simplification improves the model's performance in terms of exhibiting strong correlations in the spectrum and efficiently achieving random-matrix universality with fewer nonzero terms. Due to its simplicity and scaling properties, this model is better suited for quantum simulations of chaotic behavior and holographic metals.
Article
Materials Science, Multidisciplinary
Kazuki Yamamoto, Masaya Nakagawa, Masaki Tezuka, Masahito Ueda, Norio Kawakami
Summary: We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids in one-dimensional open quantum many-body systems by calculating correlation functions and performing finite-size scaling analysis. The results show that in the weak dissipation regime, the model belongs to the universality class characterized by the complex-valued TL parameter. As the dissipation strength increases, the model becomes massive.
