$\textit{N}$-naturalness is a novel solution to the electroweak hierarchy problem which posits $\textit{N}$ copies of the Standard Model with varying Higgs mass-squared parameters. Reheating proceeds through a “reheaton” particle that deposits most of its energy density into the Standard Model and small but potentially measurable fractions into the other copies. Typically the sector with the lightest negative Higgs mass-squared is identified as the Standard Model. We demonstrate that $\textit{N}$-naturalness admits a broader class of realizations in which the Standard Model is identified with a heavier sector, rather than being restricted to the lightest. This is made possible by resonant mixing between the reheaton and the Higgs, which generically causes one sector to be preferentially reheated and to acquire the largest share of the energy density, singling it out as the Standard Model. We demonstrate that this scenario is consistent with current cosmological bounds on new relativistic degrees of freedom and overclosure constraints from heavy stable relics, while future cosmic microwave background and high redshift surveys will probe significant portions of the remaining parameter space. Furthermore, we highlight the possibility of a novel stochastic gravitational wave spectrum from the many cosmological first order QCD phase transitions occurring across the other sectors.

United States

Brian Batell

Akshay Ghalsasi

Wenjie Huang

Matthew Low

$\textit{i}$-ncidental $\textit{N}$-naturalness

We study integrated correlation functions of half-BPS operators in SU($\textit{N}$) $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory (SYM) involving two superconformal primary operators in the stress-tensor multiplet and two identical maximal-trace operators of arbitrary $\textit{R}$-charge $\textit{p}$. Thanks to $$ \mathcal{N}=4 $$ SYM electro-magnetic duality these integrated correlators have recently been computed as exact functions of $\textit{N}$, $\textit{p}$, and of the Yang-Mills complexified coupling $\textit{τ}$. Using a combination of tools from SL(2$\textit{,}$ ℤ) spectral theory and resurgence analysis, we study the landscape of large-$\textit{N}$ and/or large-charge expansions for these correlators. In particular, we find novel non-perturbative effects in the limit where $\textit{N}$ → ∞ with $\textit{p/N}$ fixed. From a holographic point of view this double-scaling regime is deeply connected with a second family of correlators which we analyse. Using the results for the maximal-trace operators, we derive an exact expression for a new integrated correlator involving two coherent-state operators, defined via an exponential generating function of multi-graviton states. At large-$\textit{N}$ this correlator admits a holographic dual description in terms of a back-reacted geometry known as the AdS bubble. First, we show that the leading supergravity contribution to the integrated correlator agrees with a direct explicit integration of the correlator itself. Secondly, we derive predictions for the integrated version of the Virasoro-Shapiro amplitude evaluated on the AdS bubble background. Lastly, we demonstrate that the large-$\textit{N}$ non-perturbative contributions to this integrated correlator emerge from giant-magnon configurations in the dual AdS bubble

Spain

Francesco Aprile

United Kingdom

Daniele Dorigoni

Italy

Rudolfs Treilis

Dynamics of heavy operators in $$ \mathcal{N}=4 $$ SYM: integrated correlators and AdS bubbles

The feasibility of studying, numerically, properties of infinite volume QCD-like theories in the large $\textit{N}$ limit using coherent state variational methods is reassessed. An entirely new implementation of this approach is described, applicable to SU($\textit{N}$) lattice gauge theories, with or without fundamental representation fermions, on cubic lattices of up to four dimensions. In addition to various test cases, initial results are presented for Hamiltonian Yang-Mills theory on an infinite two-dimensional spatial lattice.

Laurence Yaffe

Resurrecting the coherent state variational algorithm for large $\textit{N}$ gauge theories

<p>The Cabibbo-favored decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> offers a unique window to explore unresolved puzzles in the low-energy baryon spectroscopy and the isospin dynamics of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>N</mi></math> system. Recent experimental results present a, for now, contradiction: LHCb and Belle analyses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> suggest the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>) component dominates, while the Beijing Spectrometer III (BESIII) hints at significant contributions from both isospin 0 and 1 in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> system of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math>. Furthermore, the measured branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> exceeds SU(3) symmetry predictions by a factor of 3–4, signaling strong contributions from low-lying resonances. In this work, we provide a theoretical analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> within the coupled-channel chiral unitary approach, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math> can be dynamically generated. Our calculations show a narrow peak from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi>n</mi></math> invariant mass spectrum and a distinct dip from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>n</mi></math> spectrum. The dip structure is qualitatively consistent with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math> manifestation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>N</mi><mo stretchy="false">→</mo><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>N</mi></math> scattering, supporting its molecular interpretation. This study not only connects the experimental observations but also highlights <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> as a crucial process to disentangle the nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math>. Future precise measurements of this decay channel by the BESIII, Belle II, LHCb, and the proposed Super Tau-Charm Facility are strongly encouraged.</p>

China

Meng-Yuan Li

Guan-Ying Wang

Neng-Chang Wei

De-Min Li

En Wang

Probing the isospin structure and low-lying resonances in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> decays

We set up a bootstrap approach to compute the first stringy correction to the supergravity regime of the correlation function of five 20’ operators in $$ \mathcal{N}=4 $$ super Yang-Mills. We use factorization of Mellin amplitudes, supersymmetric constraints and protected observables to refine our ansatz, leaving only a single undetermined coefficient. We identify non-protected CFT data that is sensitive to the residual ambiguity of our ansatz, and we verify the compatibility of our result with the anticipated behaviour of the Mellin amplitude in the flat-space limit. As a byproduct of our analysis, we also compute the first stringy correction to the four-point correlators of three 20’ operators and either one R-symmetry current or one stress tensor.

Joao Boas

20$\textit{′}$ five-point function of $$ \mathcal{N}=4 $$ SYM and stringy corrections

<p>We study the processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>τ</mi></msub><mi>n</mi><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mi>τ</mi><mo>−</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>−</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub><mi>p</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mi>τ</mi><mo>+</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub><mo stretchy="false">)</mo></math>, with particular emphasis on the pion energy and angular distributions, as a possible signal for lepton flavor universality violation, and in general of physics beyond the Standard Model (SM), as well as a sensitive probe of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> polarization vector. We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators. In this framework, complex Wilson coefficients which encode new physics can generate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating contributions. We propose an observable that provides a genuine <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-odd signal due to its sensitivity to particular transverse components of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> polarization vector. Namely, we show that the asymmetry in the azimuthal-angle distribution of the pion in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>τ</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>±</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math> constitutes a smoking-gun prediction of such a beyond the SM scenario. We estimate the strength of this effect extrapolating nucleon-hyperon form factors recently obtained from lattice QCD calculations.</p>

E. Hernández

J. Nieves

Sweden

J.E. Sobczyk

Probing new physics and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>τ</mi></msub><mi>n</mi><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mi>τ</mi><mo>−</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>−</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub><mi>p</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mi>τ</mi><mo>+</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></msub><mo stretchy="false">)</mo></math>

We consider planar codimension-one defects and interfaces in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory, realized by the D3/D5-brane intersection. Working in the probe limit, where the number of D5-branes is small compared to the number of D3-branes, we obtain analytic results for the holographic entanglement entropy of a ball-shaped region centered on the defect. A defect renormalization group flow is triggered by giving the defect hypermultiplets a mass, which corresponds to separating the D3- and D5-branes. Along this flow the entanglement C-function decreases monotonically. We also allow the D5-branes to carry worldvolume flux corresponding to dissolved D3-branes, in which case the setup describes an interface between two copies of $$ \mathcal{N} $$ = 4 SYM theory with different gauge groups, where an RG flow is triggered by placing one side of the interface onto the Coulomb branch. Here we again find monotonic behavior of the entanglement C-function, although its interpretation as a measure of effective degrees of freedom is problematic. We investigate possible alternative measures of degrees of freedom.

Finland

Niko Jokela

Germany

Jani Kastikainen

José Penín

Ronnie Rodgers

Helime Ruotsalainen

Entanglement C-functions of defects and interfaces in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We propose a mirror symmetry for 4d $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator algebra (VOA) describing the Schur sector (containing Higgs branch) of 4d theory, and the Coulomb branch of the effective 3d theory. The basic feature of the mirror symmetry is that many representational properties of VOA are matched with geometric properties of the Coulomb branch moduli space. Our proposal is verified for a large class of Argyres-Douglas (AD) theories engineered from M5 branes, whose VOAs are W-algebras, and Coulomb branches are the Hitchin moduli spaces. VOA data such as simple modules, Zhu’s algebra, and modular properties are matched with geometric properties like $\textit{ℂ}$ -fixed varieties in Hitchin fibers, cohomologies, and some DAHA representations. We also mention relationships to 3d symplectic duality.

Peng Shan

Dan Xie

Wenbin Yan

Mirror symmetry for circle compactified 4d $$ \mathcal{N} $$ = 2 SCFTs

Utilising the symmetry constraints of suitable topological defects, the possible RG flows of $$ \mathcal{N}=1 $$ superconformal minimal models are studied. We first employ a coset description that only captures the bosonic subalgebra, and then generalise the discussion to the actual superconformal models.

Switzerland

Matthias Gaberdiel

Lasse Merkens

Defects in $$ \mathcal{N}=1 $$ minimal models and RG flows

We focus on the use of the functional Wilsonian renormalization group framework characterized by a proper time regulator and test its use in the search of the scaling solutions and the critical properties of an $\textit{O}$($\textit{N}$)-invariant scalar field multiplet coupled to gravity in $$d=4$$ and $$d=3$$ dimensions. We employ the same background-fluctuation splitting and gauge fixing procedure, already adopted in a previous study based, instead, on the effective average action framework and a similar truncation of the effective action. Our main goal is to compare the results for the scaling solutions and some of the associated critical exponents. In this analysis, performed in a different framework, most of the picture previously uncovered is confirmed both at qualitative and quantitative level. There are, nevertheless, few differences both at finite $\textit{N}$ and in its large value limit, depending also on the schemes which in both frameworks are called “improved”.

Alfio Bonanno

Emiliano Glaviano

Gian Vacca

Proper-time functional renormalization in $\textit{O}$($\textit{N}$) scalar models coupled to gravity