Effective Theories for Nonperturbative Physics

5 Aug 2024, 09:00 → 16 Aug 2024, 16:00 Europe/Berlin

2413/2-430 - MITP Seminar Room (MITP - Mainz Institute for Theoretical Physics, Johannes Gutenberg University Mainz)

In the past decades, the Standard Model has been established to increasingly higher accuracy at experiments, which is a remarkable achievement for perturbation theory of both the strong and weak interactions. In contrast, tests for nonperturbative predictions of Standard Model physics are sorely lacking, even though nonperturbative phenomena lie at the heart of many expectations for SM and BSM physics. In particular, the role of EW sphalerons in baryogenesis, the role of QCD instantons in strong CP, and the fundamental mass gap problem of Yang-Mills theory are all commonly shared expectations about the behavior of SM physics beyond perturbation theory.

In this vein, the development of effective methods for nonperturbative calculations has a twofold role. First, nonperturbative calculations inherently predict novel and spectacular phenomena outside the realm of perturbative physics, including the production of "soft bombs" or other topological objects at collider energies. Second, the study of the mathematics of nonperturbative computations is an alternative path to making sense of the asymptotic nature of perturbative physics, a connection guaranteed by S-matrix unitarity.

This program aims to review recent progress and open new directions in the understanding of nonperturbative physics. We plan to cover nonperturbative physics in both the SM and also BSM models in the first week, while the second half of the program will discuss the "resurgence" paradigm as well as recent exact results in non-supersymmetric gauge theories. The dedicated study of nonperturbative physics in these contexts will advance our fundamental understanding of quantum field theories.

Event Pictures Download

• L1180500.jpg
• L1180509.jpg
• L1180517.jpg
• L1180524.jpg
• L1180544.jpg
• L1180547.jpg
• L1180571.jpg
• L1180599.jpg

Monday, 5 August

10:00 → 11:00 Talks

10:00 Ling-Xiao Xu - Proving chiral symmetry breaking in QCD with ’t Hooft anomaly matching

Chiral symmetry breaking in the confining phase of QCD is a well-established phenomenon, yet it has been a challenge to derive this phenomenon from the theoretical viewpoint. In the seminal 1979 Cargese lectures, ’t Hooft showed how to use anomaly matching to prove chiral symmetry breaking, he showed some but didn’t give the general proof. In this talk, I will present a new strategy which can lead to a general proof. If time permits, I will also review the strategies that have been pursed in literature and point out their limitations. This talk is based on the recent papers: hep-th/2212.02930, 2404.02971, 2404.02967.

Ling-Xiao_Xu_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

11:30 → 12:30 Talks

11:30 Álvaro Pastor Gutiérrez - Cartography of gauge-fermion dynamics: Confinement, Chiral Symmetry Breaking and Conformality

We study the interplay between colour-confining and chiral symmetry-breaking dynamics in gauge-fermion theories. We target the challenging many-flavour limit of theory space using the non-perturbative functional Renormalisation Group approach. This work connects the QCD-like regime, in quantitative agreement with Lattice data, with the perturbative conformal limit of theory space. Utilising bosonisation techniques, we obtain the theory's fundamental parameters and the relation between scales purely from first principles. Finally, we investigate interesting near-conformal theories and provide a quantitative estimate for the lower boundary of the Caswell-Bank-Zaks window. This work offers a self-consistent framework for charting the landscape of strongly interacting gauge-fermion theories necessary to reliably study strong extensions of the Standard Model of particle physics.

StrongDynamics_8_24.pdf

15:00 → 15:30 Coffee/Tea break

Tuesday, 6 August

10:00 → 11:00 Talks

10:00 Andrew Gomes - The phases of gauge theories from AMSB

Recently it has been demonstrated that anomaly-mediated supersymmetry breaking (AMSB) is a valuable tool for understanding the low-energy phases of non-SUSY gauge theories. For example, applying AMSB to SUSY SU(N) gauge theories with quarks in the fundamental leads to scalar potentials with chiral symmetry breaking minima. Furthermore, the application of AMSB to a class of SUSY SO(N) gauge theories gave the first analytic demonstration of confinement, via the dual Meissner effect, and continuous chiral symmetry breaking in a non-SUSY gauge theory. In this talk I will review these developments, and then discuss how we AMSB can be retooled to better understand dualities in 3d gauge theories. Depending on relevance and interest I can also discuss recently work on non-perturbative saddle points at large quantum number.

11:00 → 11:30 Coffee/Tea break

11:30 → 12:30 Talks

11:30 Prisco Lo Chiatto - Following Quantum Imprints in the Realm of Large Multiplicity

15:00 → 15:30 Coffee/Tea break

15:30 → 16:30 Guided discussions

15:30 Mohamed Anber - Generalized symmetries and nonperturbative physics

Wednesday, 7 August

10:00 → 11:00 Talks

10:00 Rachel Houtz - Hamiltonian Truncation Effective Theory

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. In this talk, I will show how to treat Hamiltonian truncation systematically using effective field theory methodology. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states below some energy cutoff Emax. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of 1/Emax. This method is demonstrated using 2D lambda phi^4 theory, and gives 1/Emax^2 corrections to the effective Hamiltonian. Numerical diagonalization of the effective Hamiltonian then shows residual errors of order 1/Emax^3, as expected by our power counting.

Rachel_Houtz_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

11:30 → 12:30 Talks

11:30 Werner Porod - Using gauge/gravity duality for calculations in Composite Higgs models

Werner_Porod_Mainz.pdf

15:00 → 15:30 Coffee/Tea break

Thursday, 8 August

10:00 → 11:00 Talks

10:00 Ariel Zhitnitsky - Nontrivial topology in QCD, the Vacuum Energy and Large scale magnetic field of the Universe

We discuss the   dynamics of the topologically nontrivial sectors with non-trivial holonomy in  strongly coupled QCD    in the background of the  expanding universe characterized by the Hubble scale $H\ll \Lambda_{QCD}$. We argue that the vacuum energy and the  de Sitter phase emerge dynamically with the scale $\rho_{DE}\approx  H\Lambda_{QCD}^3 \approx (10^{-3} eV)^4$, which is   amazingly close to the observed value. We argue that the key element for this idea to work is the presence of nontrivial holonomy in strongly coupled gauge theories. The effect is global in nature and cannot be formulated in terms of a gradient expansion in an effective local field theory.    We also argue that  anomalous  coupling of the dark  energy with electromagnetism  generates  the large cosmological magnetic field correlated on the scale of the visible Universe as observed. We test these ideas with solvable models for   QCD being formulated on Hyperbolic space. We also comment on some lattice QCD results when the system is formulated on a curved background modelling the expanding Universe with nonzero $H$.  We also argue that  anomalous  coupling of the dark  energy with electromagnetism  generates  the large cosmological magnetic field correlated on the scale of the visible Universe.

Ariel_Zhitnitsky_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

11:30 → 12:30 Talks

11:30 Björn Garbrecht - CP conservation in the strong interactions

There is no empirical evidence for CP conservation in the strong
interactions. As there generally is a renormalizable, parity-odd
coupling between the field strength and its dual, this requires an
explanation from theory.

I will therefore first review what interactions are present when
constructing an effective theory for hadrons from QCD. But I will also
point out, that from such considerations alone, it cannot be decided
whether the effective interactions (that, e.g., give mass to eta-prime)
are misaligned (CP violation) or aligned (no CP violation) with the
quark mass phase.

To see whether or not there is a material effect of the parity-odd
operator in QCD requires therefore an understanding of how field
configurations from different topological sectors contribute to the path
integral or, in canonical quantization, whether topology implies
different ground states that are in general not parity eigenstates. To
that end, I will review the pertinent homeomorphisms between the SU(2)
subgroups of the strong interactions and the boundaries of spacetime or
spatial hypersurfaces.

As for the Euclidean path integral approach, I will note that pure gauge
configurations on the boundary only follow when the latter is placed at
infinity. Picard-Lefschetz theory then implies that steepest-descent
integration contours cover all field configurations within a topological
sector that one can find in the infinite spacetime volume. Consequently,
the limit of infinite spacetime volume must be taken before summing over
sectors, and it turns out that parity violation then vanishes. Commuting
these limits, as tacitly done in standard approaches, corresponds to a
singular deformation of the original Cauchy contour, falsely suggesting
parity-violating results.

Regarding canonical quantization, I will note that the usually
considered theta-vacua are not properly normalizable, which is at odds
with the probability interpretation from the axioms of quantum
mechanics. The root of this problem is the summation over
gauge-redundant configurations in the orthonormality relations among
theta-vacua. Imposing that (in temporal gauge) the wave functionals and
Hilbert-space operators are well-defined when the inner product covers
each physical field configuration one time and one time only, I recover
that the consistent states satisfy Gauß' law and are moreover
eigenstates of parity.

References:
2001.07152 [hep-th]
2403.00747 [hep-th]
2404.16026 [hep-ph]

Bjoern_Garbrecht_Mainz.pdf

15:00 → 15:30 Coffee/Tea break

15:30 → 16:30 Guided discussions

15:30 Sebastian Schenk - Semiclassical Expansions and Large Quantum Numbers

Friday, 9 August

10:00 → 11:00 Talks

10:00 Mohamed Anber - Nonperturbative effects from gauging higher-form symmetries

Higher-form symmetries are pivotal in understanding the global structure of a quantum field theory. In this talk, I review the notion of higher-form symmetry in Yang-Mills theory and demonstrate that gauging it leads to nonperturbative effects. Time permitting, I will discuss two examples. First, the Standard Model possesses a 1-form global symmetry, and gauging it gives rise to new baryon- and lepton-number-violating processes. Second, the axion-Yang-Mills system features an emergent 2-form symmetry, and gauging it results in a 3-form gauge theory that correctly captures the interplay between the light (axion) and heavy (hadrons) degrees of freedom in the infrared.

Mohamed_Anber_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

Monday, 12 August

10:00 → 11:00 Talks

10:00 Matthias Carosi - Self-consistent bounce from the 2PI effective action formalism

Starting from the 2PI effective action formalism, we develop a systematic scheme to include leading radiative corrections into the evaluation of the bubble nucleation rate during a first order phase transition. This results in a system of coupled differential equations for the 1- and 2-point functions in Euclidean spacetime, which we must solve self-consistently. As a first step, we make a local extension of the Hartree approximation, which allows for a careful treatment of the translational zero modes. We discuss the renormalisation of the self-energy that must be done at every step of the iteration procedure. At last, we show numerical results for a choice of potential and parameters.

Matthias_Carosi_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

11:30 → 12:30 Talks

11:30 James Ingoldby - Hamiltonian Truncation

James_Ingoldby_Mainz.pdf

15:00 → 15:20 Coffee/Tea break

Tuesday, 13 August

10:00 → 11:00 Talks

10:00 Nils Wagner - False vacuum decay of excited states from finite-time instantons

We adapt the well-known functional instanton method to allow for the computation of excited state decay widths, efficiently bypassing the traditionally enforced infinite-time limit. With conventional instanton calculations relying on the behavior of the Euclidean propagator at late times, such investigations are, per construction, constrained to solely studying the ground state energy. By suitably projecting out the desired resonant energies using appropriate eigenfunctions, we demonstrate that the common path integral formalism can be generalized to accommodate excited state decay. We explicitly determine the sought-after decay widths, including leading quantum corrections, for arbitrary potentials, demonstrating accordance with traditional WKB results.

Nils_Wagner_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

15:00 → 15:30 Coffee/Tea break

15:30 → 16:30 Guided discussions

15:30 Otari Sakhelashvili - Theta-vacua

Wednesday, 14 August

10:00 → 11:00 Talks

10:00 Urjit Yajnik - Domain wall networks and their cosmological signatures

Several unified models that embed the SM elegantly have the possibility of domain wall formation according to Kibble mechanism. We discuss the applications to cosmology. involving gravitational waves and link of leptogenesis to EDM searches.

https://inspirehep.net/literature/2613355 ;
https://inspirehep.net/literature/1835770

Urjit_Yajnik_Mainz.pdf

11:00 → 11:30 Coffee/Tea break

15:00 → 15:30 Coffee/Tea break

Thursday, 15 August

10:00 → 11:00 Talks

10:00 Nicklas Ramberg - Gravitational Waves From Dark Confinement with Holography

Gravitational waves emitted from strongly coupled QFTs are, at present, a daunting task to accurately predict due to the strong coupling.  In this talk, we demonstrate how to predict the gravitational wave spectra of Strongly coupled QFTs using holography and lattice data input for a pure SU(N) Yang-Mills theory. We will display how holography may be useful in constructing an effective action. Once the effective action is in our grasp, we will use this to study bubble nucleation to predict the gravitational wave spectra and finally comment on other phenomenological consequences.

11:00 → 11:30 Coffee/Tea break

15:00 → 15:30 Coffee/Tea break

15:30 → 16:30 Guided discussions

15:30 Urjit Yajnik - Dissipative effects accompanying sphaleron transitions

Friday, 16 August

10:00 → 11:00 Talks

10:00 Otari Sakhelashvili - Hint to Supersymmetry from GR Vacuum

11:00 → 11:30 Coffee/Tea break