Publications

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• Anomalies in the space of coupling constants and their dynamical applications II

  Clay Cordova, Daniel S. Freed, Ho Tat Lam, Nathan Seiberg

  SciPost Phys. 8, 002 (2020) · published 7 January 2020 | Toggle abstract · pdf

  We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the $\theta$-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study $SU(N)$ and $Sp(N)$ gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the $\theta$-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

  91 citations

• Anomalies in the space of coupling constants and their dynamical applications I

  Clay Cordova, Daniel S. Freed, Ho Tat Lam, Nathan Seiberg

  SciPost Phys. 8, 001 (2020) · published 6 January 2020 | Toggle abstract · pdf

  It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincar\'{e} symmetry) to background gauge fields (and a metric for the Poincar\'{e} symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects 't Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of 't Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary 't Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized 't Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen's superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.

  99 citations

• Topological order in matrix Ising models

  Sean A. Hartnoll, Edward A. Mazenc, Zhengyan D. Shi

  SciPost Phys. 7, 081 (2019) · published 19 December 2019 | Toggle abstract · pdf

  We study a family of models for an $N_1 \times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single `spherical' constraint. In this way we generalize the results of [1] to a wide class of Ising Hamiltonians with $O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z})$ symmetry. The models can undergo topological large $N$ phase transitions in which the thermal expectation value of the distribution of singular values of the matrix $S_{aB}$ becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

  2 citations

• An introduction to spontaneous symmetry breaking

  Aron J. Beekman, Louk Rademaker, Jasper van Wezel

  SciPost Phys. Lect. Notes 11 (2019) · published 4 December 2019 | Toggle abstract · pdf

  Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes, starting from a careful definition of symmetry in physics, we introduce symmetry breaking and its consequences. Emphasis is placed on the physics of singular limits, showing the reality of symmetry breaking even in small-sized systems. Topics covered include Nambu-Goldstone modes, quantum corrections, phase transitions, topological defects and gauge fields. We provide many examples from both high energy and condensed matter physics. These notes are suitable for graduate students.

  64 citations

• An infalling observer and behind the horizon cutoff

  Amin Akhavan, Mohsen Alishahiha

  SciPost Phys. 7, 073 (2019) · published 3 December 2019 | Toggle abstract · pdf

  Using Papadodimas and Raju construction of operators describing the interior of a black hole, we present a general relation between partition functions of operators describing inside and outside the black hole horizon. In particular for an eternal black hole the partition function of the interior modes may be given in terms those partition functions associated with the modes of left and right exteriors. By making use of this relation we observe that setting a finite UV cutoff will enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff. The resultant cutoff is in agreement with what obtained in the context of holographic complexity.

  1 citation

• An index for quantum integrability

  Shota Komatsu, Raghu Mahajan, Shu-Heng Shao

  SciPost Phys. 7, 065 (2019) · published 26 November 2019 | Toggle abstract · pdf

  The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index $\mathcal{I}(J)$ for each spin $J$, with the property that $\mathcal{I}(J)$ is a lower bound on the number of quantum conserved currents of spin $J$. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the $\mathbb{CP}^{N-1}$ model, the $O(N)$ model, and the flag sigma model $\frac{U(N)}{U(1)^{N}}$. For the $O(N)$ model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current. The indices for the $\mathbb{CP}^{N-1}$ model for $N>2$ are all non-positive, consistent with the fact that these models are not integrable. The indices for the flag sigma model $\frac{U(N)}{U(1)^{N}}$ for $N>2$ are all negative. Thus, it is unlikely that the flag sigma models are integrable.

  3 citations

• Thermal decay without information loss in horizonless microstate geometries

  Iosif Bena, Pierre Heidmann, Ruben Monten, Nicholas P. Warner

  SciPost Phys. 7, 063 (2019) · published 14 November 2019 | Toggle abstract · pdf

  We develop a new hybrid WKB technique to compute boundary-to-boundary scalar Green functions in asymptotically-AdS backgrounds in which the scalar wave equation is separable and is explicitly solvable in the asymptotic region. We apply this technique to a family of six-dimensional $\frac{1}{8}$-BPS asymptotically AdS$_3\,\times\,$S$^3$ horizonless geometries that have the same charges and angular momenta as a D1-D5-P black hole with a large horizon area. At large and intermediate distances, these geometries very closely approximate the extremal-BTZ$\,\times\,$S$^3$ geometry of the black hole, but instead of having an event horizon, these geometries have a smooth highly-redshifted global-AdS$_3\,\times\,$S$^3$ cap in the IR. We show that the response function of a scalar probe, in momentum space, is essentially given by the pole structure of the highly-redshifted global-AdS$_3$ modulated by the BTZ response function. In position space, this translates into a sharp exponential black-hole-like decay for times shorter than $N_1 N_5$, followed by the emergence of evenly spaced "echoes from the cap," with period $\sim N_1 N_5$. Our result shows that horizonless microstate geometries can have the same thermal decay as black holes without the associated information loss.

  40 citations

• Why are fractional charges of orientifolds compatible with Dirac quantization?

  Yuji Tachikawa, Kazuya Yonekura

  SciPost Phys. 7, 058 (2019) · published 1 November 2019 | Toggle abstract · pdf

  Orientifold $p$-planes with $p\le4$ have fractional D$p$-charges, and therefore appear inconsistent with Dirac quantization with respect to D$(6-p)$-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the $\eta$ invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the pin+ version of the double cover of $GL(2,\mathbb{Z})$.

  36 citations

• Bulk locality and asymptotic causal diamonds

  Chethan Krishnan

  SciPost Phys. 7, 057 (2019) · published 29 October 2019 | Toggle abstract · pdf

  In AdS/CFT, the non-uniqueness of the reconstructed bulk from boundary subregions has motivated the notion of code subspaces. We present some closely related structures that arise in flat space. A useful organizing idea is that of an $asymptotic$ causal diamond (ACD): a causal diamond attached to the conformal boundary of Minkowski space. The space of ACDs is defined by pairs of points, one each on the future and past null boundaries, ${\cal I}^{\pm}$. We observe that for flat space with an IR cut-off, this space (a) encodes a preferred class of boundary subregions, (b) is a plausible way to capture holographic data for local bulk reconstruction, (c) has a natural interpretation as the kinematic space for holography, (d) leads to a holographic entanglement entropy in flat space that matches previous definitions and satisfies strong sub-additivity, and, (e) has a bulk union/intersection structure isomorphic to the one that motivated the introduction of quantum error correction in AdS/CFT. By sliding the cut-off, we also note one substantive way in which flat space holography differs from that in AdS. Even though our discussion is centered around flat space (and AdS), we note that there are notions of ACDs in other spacetimes as well. They could provide a covariant way to abstractly characterize tensor sub-factors of Hilbert spaces of holographic theories.

  5 citations

• Exceptional Chern-Simons-Matter dualities

  Clay Cordova, Po-Shen Hsin, Kantaro Ohmori

  SciPost Phys. 7, 056 (2019) · published 28 October 2019 | Toggle abstract · pdf

  We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is $(E_{N})_{1}\leftrightarrow SU(9-N)_{-1}$. Others such as $SO(3)_{8}\leftrightarrow PSU(3)_{-6},$ are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant $G_{2}$ gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

  19 citations