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We propose a novel framework to analyze symmetry breaking in dynamical systems through the lens of entropy and information transfer. Information transfer quantifies the directional exchange of entropy between observables, allowing us to anticipate the onset of symmetry breaking. For local symmetry breakings, namely, local Spontaneous Symmetry Breaking (SSB) and Dynamical Symmetry Breaking (DSB), we show that as a system loses symmetry, its trajectories exhibit a pronounced slowdown accompanied by an increase in Shannon entropy. This establishes a direct link between symmetry loss, dynamical slowing down, and entropy growth. We also extend the analysis to global symmetry breaking and characterize its associated entropy change. Finally, we demonstrate the efficacy of the proposed framework using representative examples, showing that information theoretic quantities can serve as reliable precursors and diagnostics of symmetry breaking transitions.

It is widely believed that global symmetries must be broken in Quantum Gravity. This includes higher-form symmetries, which are commonplace in supergravity coupled to vector multiplets. Recently, a quantitative criterion for the breaking of (higher-form) symmetries in effective field theories of gravity has been proposed. We studied this criterion in the context of center one-form symmetries broken by BPS states in Calabi--Yau compactifications of type IIA string theory and M-theory. In a simple toy model, we evaluated the parameters quantifying the extent of symmetry breaking for large and small values of the moduli, comparing the scales of significant breaking with other relevant physical scales.

Many supervised machine learning methods have revolutionised the empirical modelling of complex systems. These empirical models, however, are usually "black boxes" and provide only limited physical explanations about the underlying systems. Instead, so-called "knowledge discovery" methods can be used to explore the governing equations that describe observed phenomena. This paper focuses on how we can use such methods to explore underlying physics and also model a commonly observed yet not fully understood phenomenon - the breaking of ocean waves. In our work, we use symbolic regression to explore the equation that describes wave-breaking evolution from a dataset of in silico waves generated using expensive numerical methods. Our work discovers a new boundary equation that provides a reduced-order description of how the surface elevation (i.e., the water-air interface) evolves forward in time, including the instances when the wave breaks - a problem that has defied traditional approaches. Compared to the existing empirical models, the unique equation-based nature of our model allows further mathematical interpretation, which provides an opportunity to explore the fundamentals of bre

We introduce the idea of bosonic see-saw mechanism in analogy with the see-saw mechanism. Bosonic see-saw is a new symmetry breaking mechanism and we apply it to explain electroweak symmetry breaking as an inevitable consequence of supersymmetry breaking. The breaking of electroweak symmetry occurs at tree level once supersymmetry is broken. Absence of color/charge breaking in this model is related to doublet-triplet splitting in grand unified theory. An extension of MSSM with a weak triplet shows very interesting results especially when mu =0. It provides the most natural understanding of why we have only electroweak symmetry breaking rather than having color/charge breaking. In the limit mu=0, the model predicts very light chargino mass, 104 GeV while Higgs is heavy, 130 GeV.

We explore a mechanism of radiative B-L symmetry breaking in analogous to the radiative electroweak symmetry breaking. The breaking scale of B-L symmetry is related to the neutrino masses through the see-saw mechanism. Once we incorporate the U(1)_{B-L} gauge symmetry in SUSY models, the U(1)_{B-L} gaugino appears, and it can mediate the SUSY breaking (Z-prime mediated SUSY breaking) at around the scale of 10^6 GeV. Then we find a links between the neutrino mass (more precisly the see-saw or B-L scale of order 10^{6} GeV) and the Z-prime mediated SUSY breaking scale. It is also very interesting that the gluino at the weak scale becomes relatively light, and almost compressed mass spectra for the gaugino sector can be realized in this scenario, which is very interesting in scope of the LHC.

A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how spontaneous symmetry breaking may occur, and it is discussed how explicit symmetry breaking may be used to tackle certain geometric problems. A systematic study of symmetry breaking in geometry is proposed, and some preliminary thoughts on further research are formulated.

We present a comparative study of radiative electroweak symmetry breaking and conventional standard model breaking, and pose the question whether experiments can distinguish one breaking mode from the other. The importance of the problem lies in the fact that the two breaking modes have very different physical interpretations concerning the mechanism of spontaneous electroweak symmetry breaking and the origin of mass.

We build explicit supersymmetric unification models where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same sector. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and they give the soft SUSY breaking terms through the so-called gauge mediation. We investigate the mass spectrums in an explicit model with SU(5) and additional gauge groups, and discuss its phenomenological aspects. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass may be achieved by the large B-term and A-term even if the stop mass is around 1 TeV.

We show that supersymmetry breaking in a class of theories with SU(N) x SU(N-2) gauge symmetry can be studied in a calculable sigma model. We use the sigma model to show that the supersymmetry breaking vacuum in these theories leaves a large subgroup of flavor symmetries intact, and to calculate the masses of the low-lying states. By embedding the Standard Model gauge groups in the unbroken flavor symmetry group we construct a class of models in which supersymmetry breaking is communicated by both gravitational and gauge interactions. One distinguishing feature of these models is that the messenger fields, responsible for the gauge mediated communication of supersymmetry breaking, are an integral part of the supersymmetry breaking sector. We also show how, by lowering the scale that suppresses the nonrenormalizable operators, a class of purely gauge mediated models with a combined supersymmetry breaking-cum-messenger sector can be built. We briefly discuss the phenomenological features of the models we construct.

We introduce Breaking Bad, a large-scale dataset of fractured objects. Our dataset consists of over one million fractured objects simulated from ten thousand base models. The fracture simulation is powered by a recent physically based algorithm that efficiently generates a variety of fracture modes of an object. Existing shape assembly datasets decompose objects according to semantically meaningful parts, effectively modeling the construction process. In contrast, Breaking Bad models the destruction process of how a geometric object naturally breaks into fragments. Our dataset serves as a benchmark that enables the study of fractured object reassembly and presents new challenges for geometric shape understanding. We analyze our dataset with several geometry measurements and benchmark three state-of-the-art shape assembly deep learning methods under various settings. Extensive experimental results demonstrate the difficulty of our dataset, calling on future research in model designs specifically for the geometric shape assembly task. We host our dataset at https://breaking-bad-dataset.github.io/.

We introduce an explicit supersymmetric unification model where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same field. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and their loop corrections induce the soft SUSY breaking terms. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass could be achieved even if the stop mass is around 1 TeV.

Preliminary Remarks. Gauge mediated supersymmetry breaking. Gravity mediated supersymmetry breaking. Anomaly mediated supersymmetry breaking. Gaugino mediated supersymmetry breaking. Braneworld supersymmetry breaking. Conclusions.

Models of spontaneous supersymmetry breaking generically have an R-symmetry, which is problematic for obtaining gaugino masses and avoiding light R-axions. The situation is improved in models of metastable supersymmetry breaking, which generically have only an approximate R-symmetry. Based on this we argue, with mild assumptions, that metastable supersymmetry breaking is inevitable. We also illustrate various general issues regarding spontaneous and explicit R-symmetry breaking, using simple toy models of supersymmetry breaking.

We review the subject of spontaneous supersymmetry breaking. First we consider supersymmetry breaking in a semiclassical theory. We illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetry breaking. Then we give a brief review of the dynamics of supersymmetric gauge theories. Finally, we use this dynamics to present various mechanisms for dynamical supersymmetry breaking. These notes are based on lectures given by the authors in 2007, at various schools.

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the Standard Model with a generalized supersymmetry breaking sector. If the usual superpotential Yukawa couplings are forbidden by the additional gauge symmetry (such as a U(1)'), effective Dirac mass terms involving the "wrong Higgs" field can arise either at tree level due to hard supersymmetry breaking fermion Yukawa couplings, or at one-loop due to nonanalytic or "nonholomorphic" soft supersymmetry breaking trilinear scalar couplings. As both of these operators are naturally suppressed in generic models of supersymmetry breaking, the resulting neutrino masses are naturally in the sub-eV range. The neutrino magnetic and electric dipole moments resulting from the radiative mechanism also vanish at one-loop order.

We analyze supersymmetry breaking by anti-self-dual flux in the deformed conifold. This theory has been argued to be a dual realization of susy breaking by antibranes. As such, one might expect it to lead to a hierarchically small breaking scale, but only if the warp factor is taken into account. We verify this by explicitly computing the warp-modified moduli space metric. This leads to a new term, with a power-like divergence at the conifold point, which lowers the breaking scale. We finally point out various puzzles regarding the gauge theory interpretation of these results.

Several modes of $B$ decays into three pseudoscalar octet mesons PPP have been measured. These decays have provided useful information for B decays in the standard model (SM). Some of powerful tools in analyzing B decays are flavor $SU(3)$ and isospin symmetries. Such analyses are usually hampered by $SU(3)$ breaking effects due to a relatively large strange quark mass which breaks SU(3) symmetry down to isospin symmetry. The isospin symmetry also breaks down when up and down quark mass difference is non-zero. It is therefore interesting to find relations which are not sensitive to $SU(3)$ and isospin breaking effects. We find that the relations among several fully-symmetric $B \to PPP$ decay amplitudes are not affected by first order $SU(3)$ breaking effects due to a non-zero strange quark mass, and also some of them are not affected by first isospin breaking effects. These relations, therefore, hold to good precisions. Measurements for these relations can provide important information about B decays in the SM.

Symmetry breaking is a popular technique to reduce the search space for SAT solving by exploiting the underlying symmetry over variables and clauses in a formula. The key idea is to first identify sets of assignments which fall in the same symmetry class, and then impose ordering constraints, called Symmetry Breaking Predicates (SBPs), such that only one (or a small subset) of these assignments is allowed to be a solution of the original SAT formula. While this technique has been exploited extensively in the SAT literature, there is little work on using symmetry breaking for SAT Modulo Theories (SMT). In SMT, logical constraints in SAT theories are combined with another set of theory operations defined over non-Boolean variables such as integers, reals, etc. SMT solvers typically use a combination of SAT solving techniques augmented with calls to the theory solver. In this work, we take up the advances in SAT symmetry breaking and apply them to the domain of SMT. Our key technical contribution is the formulation of symmetry breaking over the Boolean skeleton variables, which are placeholders for actual theory operations in SMT solving. These SBPs are then applied over the SAT solvi

We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose-Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta.