Publications

Order by: publication date number of citations

• The algebra of anomaly interplay

  Joe Davighi, Nakarin Lohitsiri

  SciPost Phys. 10, 074 (2021) · published 25 March 2021 | Toggle abstract · pdf

  We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.

  20 citations

• Local optimization on pure Gaussian state manifolds

  Bennet Windt, Alexander Jahn, Jens Eisert, Lucas Hackl

  SciPost Phys. 10, 066 (2021) · published 11 March 2021 | Toggle abstract · pdf

  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

  9 citations

• Symmetries versus the spectrum of $ J\bar T$-deformed CFTs

  Monica Guica

  SciPost Phys. 10, 065 (2021) · published 11 March 2021 | Toggle abstract · pdf

  It has been recently shown that classical $J\bar T$ - deformed CFTs possess an infinite-dimensional Witt-Ka\v{c}-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants' energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of $J\bar T$ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semi-classical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector.

  6 citations

• Conformal field theories on deformed spheres, anomalies, and supersymmetry

  Joseph A. Minahan, Usman Naseer, Charles Thull

  SciPost Phys. 10, 063 (2021) · published 10 March 2021 | Toggle abstract · pdf

  We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to $\mathcal{N}=2$ SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the $c$ anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)$^2$ term, which we determine up to one constant by analyzing the scale dependence of various correlators in the stress-tensor multiplet. We further show that the double derivative of the free energy with respect to the marginal couplings is proportional to the two-point function of the bottom components of the marginal chiral multiplet placed at the two poles of the deformed sphere. We then use anomaly considerations and counter-terms to parametrize the finite part of the free energy which makes manifest its dependence on the K\"ahler potential. We demonstrate these results for a theory with a vector multiplet and a massless adjoint hypermultiplet using results from localization. Finally, by choosing a special value of the hypermultiplet mass where the free energy is independent of the deformation, we derive an infinite number of constraints between various integrated correlators in $\mathcal{N}=4$ super Yang-Mills with any gauge group and at all values of the coupling, extending previous results.

  4 citations

• Testing the mechanism of lepton compositeness

  Vincenzo Afferrante, Axel Maas, René Sondenheimer, Pascal Törek

  SciPost Phys. 10, 062 (2021) · published 10 March 2021 | Toggle abstract · pdf

  Strict gauge invariance requires that physical left-handed leptons are actually bound states of the elementary left-handed lepton doublet and the Higgs field within the standard model. That they nonetheless behave almost like pure elementary particles is explained by the Fr\"ohlich-Morchio-Strocchi mechanism. Using lattice gauge theory, we test and confirm this mechanism for fermions. Though, due to the current inaccessibility of non-Abelian gauged Weyl fermions on the lattice, a model which contains vectorial leptons but which obeys all other relevant symmetries has been simulated.

  4 citations

• Revisiting Wess-Zumino-Witten terms

  Yasunori Lee, Kantaro Ohmori, Yuji Tachikawa

  SciPost Phys. 10, 061 (2021) · published 10 March 2021 | Toggle abstract · pdf

  We revisit various topological issues concerning four-dimensional ungauged and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum chromodynamics (QCD), from the modern bordism point of view. We explain, for example, why the definition of the $4d$ WZW terms requires the spin structure. We also discuss how the mixed anomaly involving the 1-form symmetry of $SO$ QCD is reproduced in the low-energy sigma model.

  16 citations

• Entanglement gap, corners, and symmetry breaking

  Vincenzo Alba

  SciPost Phys. 10, 056 (2021) · published 8 March 2021 | Toggle abstract · pdf

  We investigate the finite-size scaling of the lowest entanglement gap $\delta\xi$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $\delta\xi=\Omega/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $\delta\xi=\pi^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $\Omega$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $\Omega$, at least for the case of a square corner.

  5 citations

• Matrix product operator symmetries and intertwiners in string-nets with domain walls

  Laurens Lootens, Jürgen Fuchs, Jutho Haegeman, Christoph Schweigert, Frank Verstraete

  SciPost Phys. 10, 053 (2021) · published 1 March 2021 | Toggle abstract · pdf

  We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions of its MPO symmetries amount to a set of six coupled equations that can be identified with the pentagon equations of a bimodule category. This allows us to classify all equivalent PEPS representations and build MPO intertwiners between them, synthesising and generalising the wide variety of tensor network representations of topological phases. Furthermore, we use this generalisation to build explicit PEPS realisations of domain walls between different topological phases as constructed by Kitaev and Kong [Commun. Math. Phys. 313 (2012) 351-373]. While the prevailing abstract categorical approach is sufficient to describe the structure of topological phases, explicit tensor network representations are required to simulate these systems on a computer, such as needed for calculating thresholds of quantum error-correcting codes based on string-nets with boundaries. Finally, we show that all these string-net PEPS representations can be understood as specific instances of Turaev-Viro state-sum models of topological field theory on three-manifolds with a physical boundary, thereby putting these tensor network constructions on a mathematically rigorous footing.

  30 citations

• Branes, quivers and wave-functions

  Taro Kimura, Miłosz Panfil, Yuji Sugimoto, Piotr Sułkowski

  SciPost Phys. 10, 051 (2021) · published 26 February 2021 | Toggle abstract · pdf

  We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating series, and on the other hand as wave-functions in various polarizations. We determine operations on quivers, as well as $SL(2,\mathbb{Z})$ transformations, which correspond to changing positions of these branes. Our results prove integrality of BPS multiplicities associated to this class of branes, reveal how they transform under changes of polarization, and imply all other properties of brane amplitudes that follow from the relation to quivers.

  7 citations

• The Holographic Nature of Null Infinity

  Alok Laddha, Siddharth G. Prabhu, Suvrat Raju, Pushkal Shrivastava

  SciPost Phys. 10, 041 (2021) · published 18 February 2021 | Toggle abstract · pdf

  We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space.

  78 citations