Matthew T. Walters

Universality of Long-Distance AdS Physics from the CFT Bootstrap

A bstractWe begin by explicating a recent proof of the cluster decomposition principle in AdS≥4 from the CFT≥3 bootstrap. The CFT argument also computes the leading interactions between distant objects in AdS≥4, and we confirm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit.We proceed to study the generalization to CFT2, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semiclassical, large central charge approximation, and use them to prove a suitably modified theorem. In particular, from the d = 2 bootstrap we prove the existence of large spin operators with fixed ‘anomalous dimensions’ indicative of the presence of deficit angles in AdS3. As we approach the threshold for the BTZ black hole, interpreted as a CFT2 scaling dimension, the twist spectrum of large spin operators becomes dense.Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasinormal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more refined computation of the Virasoro conformal blocks.

Virasoro Conformal Blocks and Thermality from Classical Background Fields

A bstractWe show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in AdS3, or equivalently, the eigenstate thermalization hypothesis for CFT2 at large central charge.

New light species and the CMB

A bstractWe consider the effects of new light species on the Cosmic Microwave Background. In the massless limit, these effects can be parameterized in terms of a single number, the relativistic degrees of freedom. We perform a thorough survey of natural, minimal models containing new light species and numerically calculate the precise contribution of each of these models to this number in the framework of effective field theory. After reviewing the relevant details of early universe thermodynamics, we provide a map between the parameters of any particular theory and the predicted effective number of degrees of freedom. We then use this map to interpret the recent results from the Cosmic Microwave Background survey done by the Planck satellite. Using this data, we present new constraints on the parameter space of several models containing new light species. Future measurements of the Cosmic Microwave Background can be used with this map to further constrain the parameter space of all such models.

Semiconductor probes of light dark matter

Dark matter with mass below about a GeV is essentially unobservable in conventional direct detection experiments. However, newly proposed technology will allow the detection of single electron events in semiconductor materials with significantly lowered thresholds. This would allow detection of dark matter as light as an MeV in mass. Compared to other detection technologies, semiconductors allow enhanced sensitivity because of their low ionization energy around an eV. Such detectors would be particularly sensitive to dark matter with electric and magnetic dipole moments, with a reach many orders of magnitude beyond current bounds. Observable dipole moment interactions can be generated by new particles with masses as great as 1000 TeV, providing a window to scales beyond the reach of current colliders.

Hawking from Catalan

A bstractThe Virasoro algebra determines all ‘graviton’ matrix elements in AdS3/CFT2. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT2 operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in hH/c, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation to sum the on-shell diagrams to all orders, computing the Virasoro vacuum block. Extrapolating to large hH/c determines the Hawking temperature of a BTZ black hole in dual AdS3 theories.

Eikonalization of conformal blocks

A bstractClassical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the ‘eikonalization’ of conformal blocks. We show that when an operator T appears in the OPE OxO0

A Conformal Truncation Framework for Infinite-Volume Dynamics

\mathcal{O}(x)\mathcal{O}(0)

Lightcone effective Hamiltonians and RG flows

, then the large spin Fock space states [TT ⋯ T]ℓ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an OOOO