T. Nguyen

The perturbative approach to path integrals: A succinct mathematical treatment

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick’s theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries, and we use this to study essential features of path integral manipulations, including coordinate changes, Ward identities, Schwinger-Dyson equations, Faddeev-Popov gauge-fixing, and eliminating fields by their equation of motion. We also discuss the asymptotic nature of the Wick expansion and the implications this has for defining path integrals perturbatively and nonperturbatively.

Quantization of the Nonlinear Sigma Model Revisited

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the

On discrete features of the wave equation in singular pp-wave backgrounds

O(N)

Measurements of the pp → ZZ production cross section and the Z → 4ℓ branching fraction, and constraints on anomalous triple gauge couplings at √s = 13 TeV

-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

Lagrangian correspondences and Donaldson’s TQFT construction of the Seiberg–Witten invariants of 3–manifolds

We analyze the wave equation in families of pp-wave geometries developing strong localized scale-invariant singularities in certain limits. For both cases of well-localized pp-waves and the so-called null-cosmologies, we observe an intriguing discrete dependence of the existence of a singular limit on the normalization of the pp-wave profile. We also find restrictive matching conditions relating the geometries before and after the singularity (if a singular limit for the solutions of the wave equation with initial conditions specified away from the near-singular region is assumed to exist).

Pseudorapidity distributions of charged hadrons in proton-lead collisions at

Four-lepton production in proton-proton collisions, p p → ( Z / γ ∗ ) ( Z / γ ∗ ) → 4 ℓ , where ℓ = e or μ , is studied at a center-of-mass energy of 13 TeV with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb - 1 . The ZZ production cross section, σ ( p p → Z Z ) = 17.2 ± 0.5 (stat) ± 0.7 (syst) ± 0.4 (theo) ± 0.4 (lumi) pb , measured using events with two opposite-sign, same-flavor lepton pairs produced in the mass region 60 < m ℓ + ℓ - < 120 GeV , is consistent with standard model predictions. Differential cross sections are measured and are well described by the theoretical predictions. The Z boson branching fraction to four leptons is measured to be B ( Z → 4 ℓ ) = 4 . 83 - 0.22 + 0.23 ( s t a t ) - 0.29 + 0.32 ( s y s t ) ± 0.08 ( t h e o ) ± 0.12 ( l u m i ) × 10 - 6 for events with a four-lepton invariant mass in the range 80 < m 4 ℓ < 100 GeV and a dilepton mass m ℓ ℓ > 4 GeV for all opposite-sign, same-flavor lepton pairs. The results agree with standard model predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZ γ couplings at 95% confidence level: - 0.0012 < f 4 Z < 0.0010 , - 0.0010 < f 5 Z < 0.0013 , - 0.0012 < f 4 γ < 0.0013 , - 0.0012 < f 5 γ < 0.0013 .Four-lepton production in proton-proton collisions,

5.02 and 8.16 TeV

\mathrm {p}\mathrm {p}\rightarrow (\mathrm{Z}/ \gamma ^*)(\mathrm{Z}/\gamma ^*) \rightarrow 4\ell

Quantum Yang-Mills Theory in Two Dimensions: Exact versus Perturbative

pp→(Z/γ∗)(Z/γ∗)→4ℓ, where