It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the $S$-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
Consider the effective lagrangian for pions in the chiral limit, computed to leading order in an expansion about zero temperature. To describe the scattering of pions with small momenta, it is necessary to include not just the usual shift in the pion decay constant, but also a new, nonlocal term, which is precisely analogous to the hard thermal loops of hot gauge theories.
The 1/N_c expansion for the baryon distribution amplitude is constructed in terms of a specially designed generating functional. At large N_c this functional shows exponential behavior. The exponential factor is universal for all low-lying baryons and baryon-meson scattering states. Simple factorization properties are established for the preexponential term. This factorization agrees with the large-N_c contracted SU(2N_f) spin-flavor symmetry. The consistency of the factorization with the soft-pion theorem for the baryon distribution amplitude is explicitly checked. A relation between the gene…
Finite isospin chemical potential $μ_I$ and temperature $T$ have been introduced in the framework of soft-wall AdS/QCD model. By self-consistently solve the equation of motion, we obtain the phase boundary of pion condensation phase, across which the system undergoes a phase transition between pion condensation phase and normal phase. Comparing the free energy of solutions with and without pion condensation, we find that the phase transition is of first order type both at large $μ_I$ and small $μ_I$. Qualitatively, the behavior at large $μ_I$ is in agreement with the lattice simulation in Phys…
In this paper, we investigate multi-soft behaviors of tree amplitudes in nonlinear sigma model (NLSM). The leading behaviors of amplitudes with odd number of all-adjacent soft pions are zero. We further propose and prove that leading soft factors of amplitudes with even number all-adjacent soft pions can be expressed in terms of products of the leading order Berends-Giele sub-currents in Cayley parametrization. Each sub-current in the expression contains at most one hard pion. Discussions are generalized to amplitudes containing arbitrary number of nonadjacent soft blocks: The leading behavior…
We study the phase transition between pion condensed phase and normal phase, as well as chiral phase transition in a two flavor($\mathcal{N}_f=2$) IR- improved soft-wall AdS/QCD model at finite isospin chemical potential $μ_I$ and temperature $T$. By self-consistently solving the equations of motion, we obtain the phase diagram in the plane of $μ_I$ and $T$. The pion condensation appears together with a massless Nambu-Goldstone boson $m_{π_1}(T_c, μ_I^c)=0$, which is very likely to be a second-order phase transition with mean-field critical exponents in small $μ_I$ region. When $T=0$, the crit…
Pseudo-Goldstone modes appear in many physical systems and display robust universal features. First, their mass $m$ obeys the so-called Gell-Mann-Oakes-Renner (GMOR) relation $f^2\,m^2=H\,\barσ$, with $f$ the Goldstone stiffness, $H$ the explicit breaking scale and $\barσ$ the spontaneous condensate. More recently, it has been shown that their damping $Ω$ is constrained to follow the relation $Ω=m^2 D_φ$, where $D_φ$ is the Goldstone diffusivity in the purely spontaneous phase. Pions are the most paradigmatic example of pseudo-Goldstone modes and they are related to chiral symmetry breaking in…
Spectra of pions, which are known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking, as well as their relationship with chiral phase transition and pion superfluidity phase transition, have been investigated in the framework of soft-wall AdS/QCD. In chiral limit, it is proved both numerically and analytically that pions are massless Goldstone bosons even at finite temperature, which was usually considered as an assumption in soft-wall models. Above $T_c$, at which chiral condensate $\langle \bar{q}q\rangle$ vanishes, the spectra of pions and scalar mesons merge together, s…
We study supersymmetric QCD with N_f<N_c in the limit of small supersymmetry-breaking masses and smaller quark masses using the weak-coupling Kahler potential. We calculate the full spectrum of this theory, which manifests a chiral symmetry breaking pattern similar to that caused by the strong interactions of the standard model. We derive the chiral effective lagrangian for the pion degrees of freedom, and discuss the behavior in the formal limit of large squark and gluino masses and for large N_c. We show that the resulting scalings of the pion decay constant and pion masses in these limits d…
We study the behavior of geodesics in the plane-fronted wave background of the three-dimensional (3D) gravity with propagating torsion, which possesses only massive degrees of freedom. We discover the velocity memory effect, in contrast to the current belief that its existence is due to the presence of soft particles.
The transit of a gravitating radiation pulse past arrays of detectors stationed near future null infinity in the vacuum is considered. It is shown that the relative positions and clock times of the detectors before and after the radiation transit differ by a BMS supertranslation. An explicit expression for the supertranslation in terms of moments of the radiation energy flux is given. The relative spatial displacement found for a pair of nearby detectors reproduces the well-known and potentially measurable gravitational memory effect. The displacement memory formula is shown to be equivalent t…
University of British Columbia（不列颠哥伦比亚大学）；Institut des Hautes Études Scientifiques（高等科学研究所）；Walter Burke Institute for Theoretical Physics, Caltech（加州理工学院沃尔特·伯克理论物理研究所）
Consistency relations -- which relate an N-point function to a squeezed (N+1)-point function -- are useful in large scale structure (LSS) because of their non-perturbative nature: they hold even if the N-point function is deep in the nonlinear regime, and even if they involve astrophysically messy galaxy observables. The non-perturbative nature of the consistency relations is guaranteed by the fact that they are symmetry statements, in which the velocity plays the role of the soft pion. In this paper, we address two issues: (1) how to derive the relations systematically using the residual coor…
In this work, we revisit unitary irreducible representations of the Bondi-Metzner-Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of super-momenta in addition to four-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing four-momentum, whic…
In this paper, we present a new type of electromagnetic memory. It is a `magnetic' type, or B mode, radiation memory effect. Rather than a residual velocity, we find a position displacement of a charged particle induced by the B mode radiation with memory. We find two types of electromagnetic displacement (ordinary and null). We also show that the null electromagnetic memory formulas are nothing but a Fourier transformation of soft photon theorems.
