Recursos de colección
Caltech Authors (160.918 recursos)
Repository of works by Caltech published authors.
Group = Caltech Theory
Repository of works by Caltech published authors.
Group = Caltech Theory
The geometry of a floating bridge on a drumhead soundboard produces string stretching that is first order in the amplitude of the bridge motion. This stretching modulates the string tension and consequently modulates string frequencies at acoustic frequencies. Early work in electronic sound synthesis identified such modulation as a source of bell-like and metallic timbre. And increasing string stretching by adjusting banjo string-tailpiece-head geometry enhances characteristic banjo tone. Hence, this mechanism is likely a significant source of the ring, ping, clang, and plunk common to the family of instruments that share floating-bridge/drumhead construction.
The motion of a single Fourier mode of the plucked string is an example of transient, free decay of linear, coupled, damped oscillators. It shares the rarely discussed features of the generic case, e.g., possessing a complete set of non-orthogonal eigenvectors and no normal modes, but it can be analyzed and solved analytically by hand in an approximation that is appropriate to musical instruments' plucked strings.
Kapustin, Anton; Thorngren, Ryan
We study ’t Hooft anomalies for a global discrete internal symmetry G . We construct examples of bosonic field theories in three dimensions with a nonvanishing ’t Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G_1×G_2 such that gauging G_1 necessarily breaks G_2 and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.
Lloyd, Seth; Preskill, John
Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity...
Remmen, Grant N.; Carroll, Sean M.
We address the issue of how many e-folds we would naturally expect if inflation occurred at an energy scale of order 10^(16) GeV. We use the canonical measure on trajectories in classical phase space, specialized to the case of flat universes with a single scalar field. While there is no exact analytic expression for the measure, we are able to derive conditions that determine its behavior. For a quadratic potential V(ϕ)=m^2ϕ^2/2 with m=2×10^(13) GeV and cutoff at M_(Pl)=2.4×10^(18) GeV, we find an expectation value of 2×1010 e-folds on the set of FRW trajectories. For cosine inflation V(ϕ)=Λ^4[1−cos(ϕ/f)] with f=1.5×10^(19) GeV,...
Kapustin, Anton; Seiberg, Nathan
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On ℝ^d the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify ℝ^d, and they are crucial in the context of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the...
Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well defined and can be computed using methods of topological quantum field theory. We derive a general formula for the ground-state degeneracy for Abelian fractional quantum Hall phases, including the cases when connected components of the boundary are subdivided into an arbitrary number of segments, with a different boundary condition on each segment, and in the presence of an arbitrary number of boundary domain walls.
This self-contained pedagogical simple explicit 6-step derivation of the Schwarzschild solution, in “3+1” formulation and conformal spatial gauge, (almost) avoids all affinity, curvature and index gymnastics.
Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that S^3_b partition functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2 field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional N=2 SCFTs, thus making the whole construction...
We present various (0, 2) heterotic supercurrent supermultiplets in (1 + 1) dimensional quantum field theories. From the minimal supercurrent supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz invariance, (chiral) dilatation invariance, R-invariance, (chiral) conformal invariance and their various combinations. Our construction covers many interesting and/or exotic possibilities such as Lifshitz supersymmetry and warped superconformal algebra. We also discuss the corresponding supergravity by gauging the supercurrent supermultiplet. In particular, we propose a novel class of heterotic supergravity based on the virial supercurrent.
Gadde, Abhijit; Liendo, Pedro; Rastelli, Leonardo; Yan, Wenbin
We study the integrability properties of planar N=2 superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of N=2 superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2,1|2) sector, which exists in any N=2 superconformal gauge theory, may be integrable...
Kapustin, Anton; Willett, Brian; Yaakov, Itamar
We define a class of supersymmetric defect loop operators in N = 2 gauge theories in 2 + 1 dimensions. We give a prescription for computing the expectation value of such operators in a generic N = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, Z ) action on conformal theories with abelian global symmetries.
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from...
Bélanger, Geneviève; Ellwanger, Ulrich; Gunion, John F.; Jiang, Yun; Kraml, Sabine; Schwarz, John H.
We discuss NMSSM scenarios in which the lightest Higgs boson h 1 is consistent with the small LEP excess at ~ 98 GeV in e^+ e^− → Zh with h→bb and the heavier Higgs boson h 2 has the primary features of the LHC Higgs-like signals at 125 GeV, including an enhanced γγ rate. Verification or falsification of the 98 GeV h_1 may be possible at the LHC during the 14 TeV run. The detection of the other NMSSM Higgs bosons at the LHC and future colliders is also discussed, as well as dark matter properties of the scenario under...
We discuss excitations in nonrelativistic field theories with spontaneous breaking of a continuous global symmetry. It is known that in such systems there are two types of Goldstone bosons (Type A and Type B) whose dispersion law is generically linear or quadratic, respectively. We show that Type B Goldstone bosons may have gapped partners which we call almost-Goldstone bosons. With some nondegeneracy assumption about the low-energy effective action, the total number of Goldstone and almost-Goldstone bosons adds up to the number of broken symmetry generators. We propose that deviations of the dispersion law of Goldstone bosons from linearity at small...
Kapustin, Anton; Saulina, Natalia
We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The algebraic properties of the resulting 2d RCFT, such as the classification of symmetry-preserving boundary conditions, are expressed in terms of properties of the surface operator. We show that to every surface operator one may attach a Morita-equivalence class of symmetric Frobenius algebras in the ribbon category of bulk line operators. This provides a simple interpretation of the results of Fuchs,...
Kapustin, Anton; Kim, Hyungchul; Park, Jaemo
We study dualities for N = 2 3d Chern-Simons matter theories with gauge groups U/Sp/O, matter in the two-index tensor representations (adjoint/symmetric/antisymmetric) in addition to the fundamental representation, and a superpotential. These dualities are analogous to Kutasov-Schwimmer-Seiberg dualities in 4d. We test them by computing the superconformal index and the partition function on S^3 for many dual pairs and find perfect agreement. In some cases we find a simple dual description for theories with tensor matter and no superpotential, thereby generalizing the “Duality Appetizer” of Jafferis and Yin to an infinite class of theories. We also investigate nonperturbative truncation of the chiral...
Bashkirov, Denis; Kapustin, Anton
We show that an infinite family of N=6 d=3 superconformal Chern-Simons-matter theories has hidden N=8 superconformal symmetry and hidden parity on the quantum level. This family of theories is different from the one found by Aharony, Bergman, Jafferis and Maldacena, as well as from the theories constructed by Bagger and Lambert, and Gustavsson. We also test several conjectural dualities between BLG theories and ABJ theories by comparing superconformal indices of these theories.
Bashkirov, Denis; Kapustin, Anton
We describe a method which allows one to study hidden symmetries in a large class of strongly coupled supersymmetric gauge theories in three dimensions. We apply this method to the ABJM theory and to the infrared limit of =4 SQCD with adjoint and fundamental matter. We show that the U(N) ABJM model with Chern-Simons level k = 1or k = 2 has hidden =8 supersymmetry. Hidden supersymmetry is also shown to occur in =4 d = 3 SQCD with one fundamental and one adjoint hypermultiplet. The latter theory, as well as the U(N) ABJM theory at k = 1, are...
Kapustin, Anton; Rozansky, Lev
Motivated by the path-integral analysis  of boundary conditions in a three-dimensional topological sigma model, we suggest a definition of the two-category ¨L(X) associated with a holomorphic symplectic manifold X and study its properties. The simplest objects of ¨L(X) are holomorphic lagrangian submanifolds Y ⊂ X. We pay special attention to the case when X is the total space of the cotangent bundle of a complex manifold U or a deformation thereof. In the latter case, the endomorphism category of the zero section is a monoidal category which is an A_∞ deformation of the two-periodic derived category of U.