Methods have been proposed recently to weight data in order to allow visualisation of $$C\!P$$ -violation effects in transitions of neutral $\textit{B}$ mesons to multibody final states that are not $$C\!P$$ -eigenstates. These are useful since integration of the unweighted data over the phase space would otherwise wash out the effects of interest. A similar method, elaborated upon here, with a different weighting function can also be used to visualise $$C\!P$$ -conserving $${{{B}} _{({{s}})}^0} \text {--}{{\hspace{0.0pt}\overline{\hspace{0.0pt}{B}}} _{({{s}})}^0} $$ oscillations, rather than the $$C\!P$$ -violating asymmetries. Together with the other weighting functions, this new method could be useful, for example, to demonstrate the accuracy of the calibration of the flavour tagging algorithms that are crucial for analyses such as the measurement of the $$C\!P$$ -violating phase in $${{{B}} ^0_{{s}}} \rightarrow {{{J} \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} \phi $$ decays. Their application to the formalism in common use for such decays is explicitly demonstrated.

United Kingdom

Tim Gershon

Thomas Latham

China

Switzerland

Peilian Li

France

Andy Morris

Wenbin Qian

Mark Whitehead

Italy

Ao Xu

More visualisation of decay-time-dependent asymmetries in multibody B-meson decays

By generalizing the construction of genuine multientropy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>GM</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo></mrow></msup></mrow></math> for genuine multipartite entanglement proposed in the previous paper [Genuine multi-entropy and holography, <a href="http://dx.doi.org/10.1103/714c-byxq">Phys. Rev. D 112, 026011 (2025)</a>.], we give a prescription on how to construct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>GM</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo></mrow></msup></mrow></math> systematically for any <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="monospace">q</mi></math>. The crucial point is that our construction naturally fits to the partition number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">(</mo><mi mathvariant="monospace">a</mi><mo stretchy="false">)</mo></math> of integer <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="monospace">a</mi></math>. For general <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="monospace">q</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>GM</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo></mrow></msup></mrow></math> contains <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo><mo>=</mo><mi>p</mi><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo><mo>−</mo><mi>p</mi><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>−</mo><mn>1</mn></math> number of free parameters. Furthermore, these give <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo><mo>+</mo><mn>1</mn></math> number of new diagnostics for genuine <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="monospace">q</mi></math>-partite entanglement. Especially for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="monospace">q</mi><mo>=</mo><mn>4</mn></math> case, this reproduces not only the known diagnostics pointed out by Balasubramanian et al. [Multiboundary wormholes and holographic entanglement, <a href="http://dx.doi.org/10.1088/0264-9381/31/18/185015">Classical Quantum Gravity 31, 185015 (2014)</a>.], but also a new diagnostics for quadripartite entanglement. We also study these <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>GM</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="monospace">q</mi><mo stretchy="false">)</mo></mrow></msup></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="monospace">q</mi><mo>=</mo><mn>4</mn></math>, 5 in holography and show that these are of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msub><mi>G</mi><mi>N</mi></msub><mo stretchy="false">)</mo></mrow></math> both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

Japan

Taiwan

Norihiro Iizuka

United Arab Emirates

Simon Lin

Mitsuhiro Nishida

More on genuine multientropy and holography

We study large $\textit{N}$ phase transitions in $$ \mathcal{N} $$ = 2 theories with gauge group SU($\textit{N}$) and massive hypermultiplets in diverse representations. Using supersymmetric localization we identify cases where phase transitions occur. In particular, we consider deformations of UV superconformal fixed points by giving two different masses to the fundamental hypermultiplets, and show that these theories undergo a third-order phase transition at a critical value of the ’t Hooft coupling. This provides the first example of a phase transition driven by a mass deformation of a $$ \mathcal{N} $$ = 2 superconformal field theory. We also comment on integrated correlators in these theories.

Spain

Argentina

Jeremías Aguilera-Damia

Jorge Russo

More on phase transitions in $$ \mathcal{N} $$ = 2 massive gauge theories

Recently, we used methods of arithmetic geometry to study the anomaly-free irreducible representations of an arbitrary gauge Lie algebra. Here we generalize to the case of products of irreducible representations, where it is again possible to give a complete description. A key result is that the projective variety corresponding to $\textit{m}$-fold product representations of the Lie algebra $$ {\mathfrak{su}}_n $$ is a rational variety for every $\textit{m}$ and $\textit{n}$. We study the simplest case of $$ {\mathfrak{su}}_3 $$ (corresponding to the strong interaction) in detail. We also describe the implications of a number-theoretic conjecture of Manin (and related theorems) for the number of chiral representations of bounded size $\textit{B}$ (measured roughly by the Dynkin labels) compared to non-chiral ones, giving a precise meaning to the sense in which the former (which are those most relevant for phenomenology) are rare compared to the latter. As examples, we show that, for both irreducible representations of $$ {\mathfrak{su}}_5 $$ and once-reducible product representations of $$ {\mathfrak{su}}_3 $$ that are non-anomalous, the number of chiral representations is asymptotically between $\textit{B}$(log $\textit{B}$) and $$ {B}^{\frac{4}{3}} $$ , while the number of non-chiral representations is asymptotically $\textit{B}$ . Despite this rarity of chiral, anomaly-free, product representations, we show that there are examples relevant for phenomenology, including one that gives an asymptotically-free gauge theory with Lie algebra $$ {\mathfrak{su}}_7 $$ .

Ben Gripaios

Khoi Le Nguyen Nguyen

More varieties of 4-d gauge theories: product representations

We investigate several phenomenological implications of the Weak Gravity Conjecture (WGC). We find that the WGC implies that the SM neutrinos must be electrically neutral, that the electric charge in the SM must be quantized, and that the photon must be massless. In addition, we use the WGC to set lower bounds on the electric charge of milli-charged particles (mCP), the gauge coupling of several <math altimg='si1.svg'><mi>U</mi><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></math> extensions of the SM, their kinetic mixing parameter with the SM <math altimg='si2.svg'><mi>U</mi><msub><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></mrow><mrow><mtext>EM</mtext></mrow></msub></math>, and the axion couplings to photons and fermions. We also set an upper bound on the lifetime of the proton.

India

Fayez Abu-Ajamieh

United States

Nobuchika Okada

Sudhir K. Vempati

Implications of the weak gravity conjecture on charge, kinetic mixing, the photon mass, and more

We discuss aspects of the quantum Lyapunov exponent $\textit{λ}$ in theories with an exactly marginal SYK-like random interaction, where $\textit{λ}$ can be computed as a continuous function of the interaction strength $$ \mathcal{J} $$ . In 1$\textit{d}$, we prove a conjecture from [1] which states that at small $$ \mathcal{J} $$ , $\textit{λ}$ can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the 2$\textit{d}$ version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.

Israel

Rohit Kalloor

Adar Sharon

More on chaos at weak coupling

It is well known that the area of the de Sitter cosmological horizon is related to the entropy of the bulk spacetime. Recent work has however shown that the horizon encodes more information about the bulk spacetime than just the entropy. In this work, we show that the horizon contains all of the gauge invariant (diffeomorphism and U(1)) information about (static albeit unstable) configurations of charged and rotating objects placed deep inside the de Sitter spacetime. We study highly symmetric objects, such as dipoles and cubes, built of objects with electric charge and angular momentum at their vertices. We show how these configurations affect the geometry of the cosmological horizon and imprint detailed information about the objects in the bulk onto the cosmological horizon.

Willy Fischler

Hare Krishna

Sarah Racz

There is more to the de Sitter horizon than just the area

We analyze all individual cosmic strings of various lengths in a large ensemble of the global cosmic string networks in the post-inflationary scenario, obtained from numerical simulations on a discrete lattice with $\textit{N}$ = 4096 . A strong evidence for a logarithmically growing spectral index of the string power spectrum during the evolution is newly reported as our main result. The logarithmic scaling is checked against two different approaches for generating initial random field configurations, namely fat-string type and thermal phase transition. We derive the analytic relation between two power spectra of cosmic strings and axions which should be valid under some assumptions, and the validity of those assumptions is discussed. We argue that our analytic result strongly supports the correlated spectra of cosmic strings and axions. Additionally, we initiate the statistical analysis of the causal dynamics of the cosmic strings.

South Korea

Heejoo Kim

Minho Son

More scalings from cosmic strings

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group $\textit{G}$. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD for arbitrary $\textit{G}$. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6$\textit{j}$-symbols of $\textit{G}$. For $\textit{G}$ = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6$\textit{j}$-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

Ross Dempsey

Silviu Pufu

Benjamin Søgaard

Igor Klebanov

More about the lattice Hamiltonian for Adjoint QCD

We extract the complex frequency of the lowest quasinormal mode (QNM) from the holographically computed entropy density near thermodynamic equilibrium. The system under study is a purely thermal supersymmetric Yang-Mills <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> plasma undergoing homogeneous isotropization dynamics. Starting from a far-from-equilibrium initial state, the system evolves toward equilibrium entropy, forming a stairway pattern. Our analysis reveals that the rate of increase of the stairway is twice the decay rate (imaginary part) of the lowest QNM. Based on this observation, we propose a model that explains how this information is encoded in the entropy. The model is further extended to include finite temperature, R-charge density, and scalar condensate, revealing an additional feature: the system’s dominant dissipation channel may shift to one driven by the scalar condensate, depending on the chemical potential.