General anomaly matching by Goldstone bosons

We describe how Goldstone bosons of spontaneous symmetry breaking G → H can reproduce anomalies of UV theories under the symmetry group G at the nonpertur- bative level. This is done by giving a general definition of Wess-Zumino-Witten terms in terms of the invertible field theories in d + 1 dimensions which describe the anomalies of d-dimensional UV theories. The hidden local symmetry $$ \hat{H} $$ H ̂ , which is used to describe Goldstone bosons in coset construction G/H , plays an important role. Our definition also naturally leads to generalized θ-angles of the hidden local gauge group $$ \hat{H} $$ H ̂ . We illustrate this point by SO(Nc) (or Spin(Nc)) QCD-like theories in four dimensions.

The cosmological phonon: symmetries and amplitudes on sub-horizon scales

In contrast to massless spinning particles, scalars are not heavily constrained by unitarity and locality. Off-shell, no gauge symmetries are required to write down manifestly local theories, while on-shell consistent factorisation is trivial. Instead a useful classification scheme for scalars is based on the symmetries they can non-linearly realise. Motivated by the breaking of Lorentz boosts in cosmology, in this paper we classify the possible symmetries of a shift-symmetric scalar that is assumed to non-linearly realise Lorentz boosts as, for example, in the EFT of inflation. Our classification method is algebraic; guided by the coset construction and inverse Higgs constraints. We rediscover some known phonon theories within the superfluid and galileid classes, and discover a new galileid theory which we call the extended galileid. Generic galileids correspond to the broken phase of galileon scalar EFTs and our extended galileids correspond to special subsets where each galileon coupling is fixed by an additional symmetry. We discuss the broken phase of theories that also admit a perturbation theory around Poincaré invariant vacua and we show that the so-called exceptional EFTs, the DBI scalar and special galileon, do not admit such a broken phase. Concentrating on DBI we provide a detailed account of this showing that the scattering amplitudes are secretly Poincaré invariant when the theory is expanded around the superfluid background used in the EFT of inflation. We point out that DBI is an exception to the common lore that the residue of the total energy pole of cosmological correlators is proportional to the amplitude. We also discuss the inevitability of poles in 2 → 2 scattering amplitudes when boost are spontaneously broken meaning that such theories do not admit Adler zeros and generalisations even in the presence of a shift symmetry.

The 𝒩 = 4 coset model and the higher spin algebra

By computing the operator product expansions between the first two [Formula: see text] higher spin multiplets in the unitary coset model, the (anti-)commutators of higher spin currents are obtained under the large [Formula: see text] ’t Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti-)commutators for generic spins [Formula: see text] and [Formula: see text] with manifest [Formula: see text] symmetry at vanishing ’t Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the [Formula: see text] [Formula: see text] algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two [Formula: see text] invariant tensors. We also describe the [Formula: see text] higher spin generators, by using the above coset construction results, for general superspin [Formula: see text] in terms of oscillators in the matrix generalization of [Formula: see text] Vasiliev higher spin theory at nonzero ’t Hooft-like coupling constant. We obtain the [Formula: see text] higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins [Formula: see text] and [Formula: see text].

Coset construction of Virasoro minimal models and coupling of Wess–Zumino–Witten theory with Schramm–Loewner evolution

Schramm–Loewner evolution (SLE) is a random process that gives a useful description of fractal curves. After its introduction, many works concerning the connection between SLE and conformal field theory (CFT) have been carried out. In this paper, we develop a new method of coupling SLE with a Wess–Zumino–Witten (WZW) model for [Formula: see text], an example of CFT, relying on a coset construction of Virasoro minimal models. Generalizations of SLE that correspond to WZW models were proposed by previous works [E. Bettelheim et al., Stochastic Loewner evolution for conformal field theories with Lie group symmetries, Phys. Rev. Lett. 95 (2005) 251601] and [Alekseev et al., On SLE martingales in boundary WZW models, Lett. Math. Phys. 97 (2011) 243–261], in which the parameters in the generalized SLE for [Formula: see text] were related to the level of the corresponding [Formula: see text]-WZW model. The present work unveils the mechanism of how the parameters were chosen, and gives a simpler proof of the result in these previous works, shedding light on a new perspective of SLE/WZW coupling.

Spontaneous breaking of (2 + 1)-dimensional Lorentz symmetry by an antisymmetric tensor

One kind of spontaneous (2 + 1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is SO(2, 1) [Formula: see text] SO(1, 1). Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu–Goldstone bosons is obtained.