5,091 research outputs found
Insertions Yielding Equivalent Double Occurrence Words
A double occurrence word (DOW) is a word in which every symbol appears
exactly twice; two DOWs are equivalent if one is a symbol-to-symbol image of
the other. We consider the so called repeat pattern () and the
return pattern (), with gaps allowed between the 's.
These patterns generalize square and palindromic factors of DOWs, respectively.
We introduce a notion of inserting repeat/return words into DOWs and study how
two distinct insertions into the same word can produce equivalent DOWs. Given a
DOW , we characterize the structure of which allows two distinct
insertions to yield equivalent DOWs. This characterization depends on the
locations of the insertions and on the length of the inserted repeat/return
words and implies that when one inserted word is a repeat word and the other is
a return word, then both words must be trivial (i.e., have only one symbol).
The characterization also introduces a method to generate families of words
recursively
Sequential weak measurement
The notion of weak measurement provides a formalism for extracting
information from a quantum system in the limit of vanishing disturbance to its
state. Here we extend this formalism to the measurement of sequences of
observables. When these observables do not commute, we may obtain information
about joint properties of a quantum system that would be forbidden in the usual
strong measurement scenario. As an application, we provide a physically
compelling characterisation of the notion of counterfactual quantum
computation
Transformations of Spherical Blocks
We further explore the correspondence between N=2 supersymmetric SU(2) gauge
theory with four flavors on epsilon-deformed backgrounds and conformal field
theory, with an emphasis on the epsilon-expansion of the partition function
natural from a topological string theory point of view. Solving an appropriate
null vector decoupling equation in the semi-classical limit allows us to
express the instanton partition function as a series in quasi-modular forms of
the group Gamma(2), with the expected symmetry Weyl group of SO(8) semi-direct
S_3. In the presence of an elementary surface operator, this symmetry is
enhanced to an action of the affine Weyl group of SO(8) semi-direct S_4 on the
instanton partition function, as we demonstrate via the link between the null
vector decoupling equation and the quantum Painlev\'e VI equation.Comment: 31 pages, 1 figure; v2: typos corrected, references adde
Majorana dimers and holographic quantum error-correcting codes
Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography
Double-soft behavior of the dilaton of spontaneously broken conformal invariance
The Ward identities involving the currents associated to the spontaneously
broken scale and special conformal transformations are derived and used to
determine, through linear order in the two soft-dilaton momenta, the
double-soft behavior of scattering amplitudes involving two soft dilatons and
any number of other particles. It turns out that the double-soft behavior is
equivalent to performing two single-soft limits one after the other. We confirm
the new double-soft theorem perturbatively at tree-level in a -dimensional
conformal field theory model, as well as nonperturbatively by using the
"gravity dual'' of super Yang-Mills on the Coulomb branch; i.e.
the Dirac-Born-Infeld action on AdS.Comment: 48 pages, one appendi
Acrostic Dictionary of Wordplay Terms
A bunch of definitive reverse acrostics presented in February (\u2710-8) included seven wordplay terms, with especially fun ones for logology and logophile. I thought a rather immoderate list of wordplay terms similarly defined might be appreciated by logology fans. Read the definitions first. If they are not clear, then consult the examples, which are given as answers if needed
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