2,475 research outputs found
Fluctuation theorems, quantum channels and gravitational algebras
No full textAbstract In this note we study nonequilibrium fluctuations in gravitational algebras within de Sitter space. An essential aspect of this study is quantum measurement theory, which allows us to access the dynamical fluctuations of observables via a two-point measurement scheme. Using this formalism, we establish specific fluctuation theorems. Additionally, we demonstrate that quantum channels are represented by subfactors, using the relationship between measurement theory and quantum channels. We also comment on implementing a quantum channel using Jones’ theory of subfactors
Hodge-Elliptic Genera, K3 Surfaces and Enumerative Geometry
No full textK3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences in black hole physics and in number theory. To a K3 surface, string theory associates an Elliptic genus, a certain partition function directly related to the theory of Jacobi modular forms. A multiplicative lift of the Elliptic genus produces another modular object, an Igusa cusp form, which is the generating function of BPS invariants of K3×E. In this note, we will discuss a refinement of this chain of ideas. The Elliptic genus can be generalized to the so-called Hodge-Elliptic genus which is then related to the counting of refined BPS states of K3×E. We show how such BPS invariants can be computed explicitly in terms of different versions of the Hodge-Elliptic genus, sometimes in closed form, and discuss some generalizations
BPS Spectra, Barcodes and Walls
No full textBPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper we approach this problem from the perspective of persistent homology. Persistent homology is at the base of topological data analysis, which aims at extracting topological features out of a set of points. We use these techniques to investigate the topological properties which characterize the spectra of several supersymmetric models in field and string theory. We discuss how such features change upon crossing walls of marginal stability in a few examples. Then we look at the topological properties of the distributions of BPS invariants in string compactifications on compact threefolds, used to engineer black hole microstates. Finally we discuss the interplay between persistent homology and modularity by considering certain number theoretical functions used to count dyons in string compactifications and by studying equivariant elliptic genera in the context of the Mathieu moonshine
Quantum line defects and refined BPS spectra
No full textIn this note, we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class . Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR, they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the K-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular, refined framed BPS states are described via Euler characteristics of certain complexes of sheaves
On the M2-Brane Index on Noncommutative Crepant Resolutions
No full textOn certain M-theory backgrounds which are a circle fibration over a smooth
Calabi-Yau, the quantum theory of M2 branes can be studied in terms of the
K-theoretic Donaldson-Thomas theory on the threefold. We extend this relation
to noncommutative crepant resolutions. In this case the threefold develops a
singularity and classical smooth geometry is replaced by the algebra of paths
of a certain quiver. K-theoretic quantities on the quiver representation moduli
space can be computed via toric localization and result in certain rational
functions of the toric parameters. We discuss in particular the case of the
conifold and certain orbifold singularities.Comment: 38 pages, two Mathematica notebooks are included with the paper; v2
typos corrected; v3 typos corrected, presentation improved, published versio
A note on discrete dynamical systems in theories of class S
No full textIn this note we consider the set of line operators in theories of class S. We
show that this set carries the action of a natural discrete dynamical system associated with
the BPS spectrum. We discuss several applications of this perspective; the relation with
global properties of the theory; the set of constraints imposed on the spectrum generator,
in particular for the case of SU(2) N = 2∗
; and the relation between line defects and certain
spherical Double Affine Hecke Algebras
Equiatomic ternary lanthanum-transition metal-tin phases: Structural and electrical results
No full textThe crystallographic parameters and electrical resistivity measurements in the 1.5–300 K temperature range for the LaXSn phases (X ≡ Rh, Ir, Ni, Pd, Pt, Cu, Ag, Au) are reported. A change in structure with increasing group number of the transition metal is observed. A new superconducting compound, LaRhSn with Tc = 1.7 K, is detected by electrical resistivity measurements and confirmed by a.c. susceptibility data. A negative curvature in the thermal dependence of the electrical resistivity is observed for all compounds. A quantitative analysis of the experimental data using Mott's model and the phenomenological exponential approach is reported
Persistent homology and string vacua
No full textWe use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homological characteristics persist over a long range of scales. We apply these techniques in several contexts. We analyze N=2 vacua by focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg models. We then turn to flux compactifications and discuss how we can use topological data analysis to extract physical information. Finally we apply these techniques to certain phenomenologically realistic heterotic models. We discuss the possibility of characterizing string vacua using the topological properties of their distributions
Gravitational F-terms of SO/Sp gauge theories and anomalies
No full textWe study the first non trivial gravitational corrections to the F-terms of N = 1 SYM SO/Sp gauge theories, with matter in some representations, by using the generalized Konishi anomaly method. We derive equations at genus one for the operators in the chiral ring and compare them with the loop equations of the corresponding matrix models, finding agreement. We find that for adjoint representation the genus 0 contributions to such corrections can be adsorbed by a field redefinition; remarkably, this is not the case for matter in the (anti-) symmetric representation of (Sp) SO. © SISSA/ISAS 2003
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