Nonrelativistic Corners of N=4{\cal N} = 4 Supersymmetric Yang--Mills Theory

We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1) \times \text{U}(1)$ invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the $\text{SU}(1,1)$ sector, establishing the consistency of the limit at the quantum level. We discover a tantalizing field-theoretic structure, corresponding to a $(1+1)$-dimensional complex chiral boson on a circle coupled to a nondynamical gauge field, both in the adjoint representation of $\text{SU}(N)$. The successful construction of a lower-dimensional nonrelativistic field theory in the $\text{SU}(1,1)$ near-BPS limit provides a proof of concept for other BPS bounds. These are expected to lead to richer field theories in nonrelativistic corners of ${\cal N} = 4$ SYM that include fermions, gauge fields and supersymmetry and can provide a novel path towards understanding strongly coupled finite-$N$ dynamics of gauge theories.Comment: 6 pages, 1 figure; v2: minor clarifications added, matches journal versio

Massive spin-2 theories

We give an introduction to massive spin-2 theories and the problem of their non-linear completion. We review the Boulware-Deser ghost problem and two ways to circumvent classic no-go theorems. In turn, massive spin-2 theories are not uniquely defined. In the case of truncated theories, we show that the Boulware-Deser ghost may only be avoided if the derivative structure of the theory is not tuned to be Einsteinian.Comment: 14 pages - Invited review for the Central European Journal of Physics, topical issue devoted to "Cosmology and Particle Physics beyond Standard Models". v2: References added, extended discussion on massive gravit

Self-unitarization of New Higgs Inflation and compatibility with Planck and BICEP2 data

In this paper we show that the Germani-Kehagias model of Higgs inflation (or New Higgs Inflation), where the Higgs boson is kinetically non-minimally coupled to the Einstein tensor is in perfect compatibility with the latest Planck and BICEP2 data. Moreover, we show that the tension between the Planck and BICEP2 data can be relieved within the New Higgs inflation scenario by a negative running of the spectral index. Regarding the unitarity of the model, we argue that it is unitary throughout the evolution of the Universe. Weak couplings in the Higgs-Higgs and Higgs-graviton sectors are provided by a large background dependent cut-off scale during inflation. In the same regime, the W and Z gauge bosons acquire a very large mass, thus decouple. On the other hand, if they are also non-minimally coupled to the Higgs boson, their effective masses can be enormously reduced. In this case, the W and Z bosons are no longer decoupled. After inflation, the New Higgs model is well approximated by a quartic Galileon with a renormalizable potential. We argue that this can unitarily create the right conditions for inflation to eventually start.Comment: 14 pages, 1 figure. [v2]: Explanations added, minor changes, results unchanged. Version published in JCA

Nambu-Goldstone Effective Theory of Information at Quantum Criticality

We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point we develop a new method by mapping a Bose-Einstein condensate of $N$-particles onto a sigma model with a continuous global (pseudo)symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe the information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-$N$ limit and the total information-storage capacity increases with $N$ either exponentially or as a power law. The longevity of information-storage also increases with $N$, whereas the scrambling time in the over-critical regime is controlled by the Lyapunov exponent and scales logarithmically with $N$. This connection reveals that the origin of black hole information storage lies in the quantum criticality of the graviton Bose-gas, and that much simpler systems that can be manufactured in table-top experiments can exhibit very similar information-processing dynamics.Comment: 25 pages, 6 figure

Probing emergent geometry through phase transitions in free vector and matrix models

Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N) or U(N) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at finite temperature and large N phase transitions even at vanishing 't Hooft coupling. At low temperature, the leading behavior of boundary two-point functions is consistent with propagation through a bulk thermal anti de Sitter space. Above the phase transition, the two-point function shows significant departure from thermal AdS space and the emergence of localized black hole like objects in the bulk. In adjoint models, these objects appear at length scales of order of the AdS radius, consistent with a Hawking-Page transition, but in vector models they are parametrically larger than the AdS scale. In low dimensions, we find another crossover at large distances beyond which the correlation function again takes a thermal AdS form, albeit with a temperature dependent normalization factor.Comment: 24 pages, 1 table, 3 figure