MIT Center for Theoretical Physics – a Leinweber Institute

Physics beyond the Standard Model, whether of primordial or post-inflationary origin, can leave scale-dependent signals in the anisotropies of the Cosmic Microwave Background (CMB). In this work, we study how distinguishable these broad classes of signals are and quantify their level of degeneracy. In this initial investigation, for primordial features, we limit ourselves to those of the ``sharp'' and ``resonant'' kinds; for post-inflationary features, we consider two qualitatively distinct models: exotic energy injection, which deposits energy into the primordial plasma and modifies the global thermodynamic history, and early dark energy (EDE), which affects the CMB through the background expansion and gravitational perturbations. By studying representative examples, we find that while primordial features can leave oscillatory signatures in the CMB power spectrum with essentially arbitrary frequency and running, the post-inflationary models considered here produce qualitatively different patterns that cannot generically reproduce the characteristic running of primordial feature oscillations. We verify these findings first with a principal component analysis, and show using only the most significant principal components that there are no significant degeneracies between the primordial and post-inflationary features considered here, and secondly with a full likelihood analysis, which shows that the resulting posteriors do not change significantly when considering individual classes of models or combinations of primordial/post-inflationary features. While the two post-inflationary models probe distinct physical mechanisms and both are implemented in a simplified, phenomenological fashion, the methods used in this work can be generalized to include more realistic signals or other classes of signals.

We study the sensitivity of future 10 TeV plasma wakefield colliders to a real electroweak singlet scalar $S$ coupled to the Standard Model through the Higgs portal. Using luminosity spectra obtained from particle-in-cell simulations, we compare $e^+e^-$ and $e^-e^-$ configurations with both flat and round beam profiles, as well as a $γγ$ collider based on Compton backscattering of laser photons off the $e^-e^-$ beams. The $e^-e^-$ and $γγ$ options avoid the open challenge of accelerating positrons in plasma. Without a positron beam, however, the vector boson fusion channels $e^+e^-toνbarνS$ and $e^+e^-toνbarνSS$, which dominate at $e^+e^-$ colliders, can only proceed through secondary positrons and are heavily suppressed. At a $γγ$ collider, this loss in signal rate is partially compensated by additional photon-initiated processes. While the $e^-e^-$ configurations are not as competitive, both the $e^+e^-$ and $γγ$ wakefield options have a reach qualitatively similar to that of a 10 TeV muon collider and the FCC-hh. Between the two, the $γγ$ option gives the stronger sensitivity if the achievable geometric luminosities of $e^+e^-$ colliders are more than a factor of $sim$3 lower than that of the $γγ$ collider.

We numerically study the space of compact unitary two-dimensional conformal field theories (2d CFTs) with central charge $c>1$ using the modular bootstrap. We focus on bounding the spectral gap $Δ_{rm gap}$ of such theories, namely the smallest scaling dimension among the non-vacuum primary operators. We use both a primal method that directly searches for consistent spectra and a dual method that yields rigorous exclusions. A key feature of our analysis is requiring the degeneracies of primary operators to be positive integers. At $c$ very near $1$, the integrality constraint greatly reduces the allowed spectral gap in both methods. For example, at $c-1 = 3times 10^{-3}$ integrality strengthens the rigorous bound from $Δ_{rm gap} lesssim 0.5$ to $Δ_{rm gap} < 0.041$. Our results suggest that the spectral gap might vanish as $c$ approaches $1$ from above.

We construct an exact map between continuum fermion fields and lattice fields in 1+1 dimensions. This map rewrites a continuum Hamiltonian as a lattice Hamiltonian with nearest-neighbor couplings and an infinite-dimensional local Hilbert space. The resulting lattice model reproduces exactly the energy spectrum, global operator algebra, chiral symmetries, and anomalies of the continuum QFT on any finite lattice. Unlike domain wall fermions, truncating the local Hilbert space introduces no extra massless modes, and the entanglement entropy of an interval converges as the truncation is removed. The lattice local algebras are of type I and lie between the type III continuum algebras of nested spatial regions, in accordance with the split property. We demonstrate this construction explicitly for $N$ Majorana fermions, realizing the $mathrm{O}(N)_mathrm{L}timesmathrm{O}(N)_mathrm{R}$ lattice chiral symmetry. We also construct an exact lattice model for the Schwinger model and numerically reproduce the mass gap $e/sqrtπ$.