arXiv subjects

Ziqi Yan

Publications and source records attributed to Ziqi Yan.

45 records · Page 3Linked to original sources

arXiv2019

An Action for Extended String Newton-Cartan Gravity

We construct an action for four-dimensional extended string Newton-Cartan gravity which is an extension of the string Newton-Cartan gravity that underlies nonrelativistic string theory. The action can be obtained as a nonrelativistic limit of the Einstein-Hilbert action in General Relativity augmented with a term that contains an auxiliary two-form and one-form gauge field that both have zero flux on-shell. The four-dimensional extended string Newton-Cartan gravity is based on a central extension of the algebra that underlies string Newton-Cartan gravity. The construction is similar to the earlier construction of a three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which is based on a central extension of the algebra that underlies Newton-Cartan gravity. We show that this three-dimensional action is naturally obtained from the four-dimensional action by a reduction over the spatial isometry direction longitudinal to the string followed by a truncation of the extended string Newton-Cartan gravity fields. Our construction can be seen as a special case of the construction of an action for extended p-brane Newton-Cartan gravity in p+3 dimensions.

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arXiv2019

Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence

We find a Polyakov-type action for strings moving in a torsional Newton-Cartan geometry. This is obtained by starting with the relativistic Polyakov action and fixing the momentum of the string along a non-compact null isometry. For a flat target space, we show that the world-sheet theory becomes the Gomis-Ooguri action. From a target space perspective these strings are non-relativistic but their world-sheet theories are still relativistic. We show that one can take a scaling limit in which also the world-sheet theory becomes non-relativistic with an infinite-dimensional symmetry algebra given by the Galilean conformal algebra. This scaling limit can be taken in the context of the AdS/CFT correspondence and we show that it is realized by the `Spin Matrix Theory' limits of strings on AdS$_5$ $\times$ $S^5$. Spin Matrix theory arises as non-relativistic limits of the AdS/CFT correspondence close to BPS bounds. The duality between non-relativistic strings and Spin Matrix theory provides a holographic duality of its own and points towards a framework for more tractable holographic dualities whereby non-relativistic strings are dual to near BPS limits of the dual field theory.

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arXiv2018

Nonrelativistic String Theory and T-Duality

Nonrelativistic string theory in flat spacetime is described by a two-dimensional quantum field theory with a nonrelativistic global symmetry acting on the worldsheet fields. Nonrelativistic string theory is unitary, ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying nonrelativistic symmetry. The worldsheet theory of nonrelativistic string theory is coupled to a curved spacetime background and to a Kalb-Ramond two-form and dilaton field. The appropriate spacetime geometry for nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is distinct from Riemannian geometry. This defines the sigma model of nonrelativistic string theory describing strings propagating and interacting in curved background fields. We also implement T-duality transformations in the path integral of this sigma model and uncover the spacetime interpretation of T-duality. We show that T-duality along the longitudinal direction of the string Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This relation provides a first principles definition of string theory in the discrete light cone quantization (DLCQ) in an arbitrary background, a quantization that appears in nonperturbative approaches to quantum field theory and string/M-theory, such as in Matrix theory. T-duality along a transverse direction of the string Newton-Cartan geometry equates nonrelativistic string theory in two distinct, T-dual backgrounds.

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arXiv2017

Quantization of Horava Gravity in 2+1 Dimensions

We study quantum corrections to projectable Horava gravity with $z = 2$ scaling in 2+1 dimensions. Using the background field method, we utilize a non-singular gauge to compute the anomalous dimension of the cosmological constant at one loop, in a normalization adapted to the spatial curvature term.

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arXiv2017

PrivMin: Differentially Private MinHash for Jaccard Similarity Computation

In many industrial applications of big data, the Jaccard Similarity Computation has been widely used to measure the distance between two profiles or sets respectively owned by two users. Yet, one semi-honest user with unpredictable knowledge may also deduce the private or sensitive information (e.g., the existence of a single element in the original sets) of the other user via the shared similarity. In this paper, we aim at solving the privacy issues in Jaccard similarity computation with strict differential privacy guarantees. To achieve this, we first define the Conditional $ε$-DPSO, a relaxed differential privacy definition regarding set operations, and prove that the MinHash-based Jaccard Similarity Computation (MH-JSC) satisfies this definition. Then for achieving strict differential privacy in MH-JSC, we propose the PrivMin algorithm, which consists of two private operations: 1) the Private MinHash Value Generation that works by introducing the Exponential noise to the generation of MinHash signature. 2) the Randomized MinHashing Steps Selection that works by adopting Randomized Response technique to privately select several steps within the MinHashing phase that are deployed with the Exponential mechanism. Experiments on real datasets demonstrate that the proposed PrivMin algorithm can successfully retain the utility of the computed similarity while preserving privacy.

cs.DS↗

arXiv2016

Nonrelativistic Short-Distance Completions of a Naturally Light Higgs

Nonrelativistic scalar field theories can exhibit a natural cascading hierarchy of scales, protected by a hierarchy of polynomial shift symmetries. Using a simple model, we argue that a high-energy cross-over to such nonrelativistic behavior naturally leads to light scalars, and thus represents a useful ingredient for technically natural resolutions of scalar mass hierarchies, perhaps even the Higgs mass hierarchy puzzle.

hep-ph↗

arXiv2015

Scalar Field Theories with Polynomial Shift Symmetries

We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree $P$, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree $P$? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of $P=1$ (essentially equivalent to Galileons), we reproduce the known Galileon $N$-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with $N$ vertices. Then we extend the classification to $P>1$ and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.

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arXiv2015

Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking

Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion $ω\sim k^n$ ($n=2,3,\ldots$), whose naturalness is protected by polynomial shift symmetries. Here we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of $n$ changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.

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arXiv2013

Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons

We investigate spontaneous global symmetry breaking in the absence of Lorentz invariance, and study technical Naturalness of Nambu-Goldstone (NG) modes whose dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents $z>1$. For example, we find NG modes with a technically natural quadratic dispersion relation which do not break time reversal symmetry and are associated with a single broken symmetry generator, not a pair. The mechanism is protected by an enhanced `polynomial shift' symmetry in the free-field limit.

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