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Peng Gao

Publications and source records attributed to Peng Gao.

At least 505 records · Page 28Linked to original sources
arXiv2010

Minimal surfaces in AdS space and Integrable systems

We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS$_5$. The Lax pair for the reduced theory is found, and written entirely in terms of the $A_3=D_3$ root system, generalizing the $B_2$ affine Toda system which appears for the AdS$_4$ string. For the $B_2$ affine Toda system, we show that the area of the worlsheet is obtainable from the moduli space Kähler potential of a related Hitchin system. We also explore the Saveliev-Leznov construction for solutions of the $B_2$ affine Toda system, and recover the rotationally symmetric solution associated to Painleve transcendent.

hep-th↗
arXiv2010

One level density of low-lying zeros of families of $L$-functions

In this paper, we prove some one level density results for low-lying zeros of families of $L$-functions. More specifically, the families under consideration are that of $L$-functions of holomorphic Hecke eigenforms of level 1 and weight $k$ twisted with quadratic Dirichlet characters and that of cubic and quartic Dirichlet $L$-functions.

math.NT↗
arXiv2009

On weighted remainder form of Hardy-type inequalities

We use different approaches to study a generalization of a result of Levin and Stečkin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type inequalities.

math.FA↗
arXiv2009

On lower and upper bounds of matrices

Using an approach of Bergh, we give an alternate proof of Bennett's result on lower bounds for non-negative matrices acting on non-increasing non-negative sequences in $l^p$ when $p \geq 1$ and its dual version, the upper bounds when $0<p \leq 1$. We also determine such bounds explicitly for some families of matrices.

math.FA↗
arXiv2009

The second moment of Dirichlet twists of Hecke $L$-functions

Fix a Hecke cusp form $f$, and consider the $L$-function of $f$ twisted by a primitive Dirichlet character. As we range over all primitive characters of a large modulus $q$, what is the average behavior of the square of the central value of this $L$-function? Stefanicki proved an asymptotic valid only for $q$ having very few prime factors, and we extend this to almost all $q$.

math.NT↗
arXiv2008

Abelian Fibrations, String Junctions, and Flux/Geometry Duality

In previous work, it was argued that the type IIB T^6/Z_2 orientifold with a choice of flux preserving N=2 supersymmetry is dual to a class of purely geometric type IIA compactifications on abelian surface (T^4) fibered Calabi-Yau threefolds. We provide two explicit constructions of the resulting Calabi-Yau duals. The first is a monodromy based description, analogous to F-theory encoding of Calabi-Yau geometry via 7-branes and string junctions, except for T^4 rather than T^2 fibers. The second is an explicit algebro-geometric construction in which the T^4 fibers arise as the Jacobian tori of a family of genus-2 curves. This improved description of the duality map will be a useful tool to extend our understanding of warped compactifications. We sketch applications to related work to define warped Kaluza-Klein reduction in toroidal orientifolds, and to check the modified rules for D-brane instanton zero mode counting due to the presence of flux and other D-branes. The nontrivial fundamental groups of the Calabi-Yau manifolds constructed also have potential applications to heterotic model building.

hep-th↗
arXiv2008

On l^p norms of weighted mean matrices

We study $l^{p}$ operator norms of weighted mean matrices using the approaches of Kaluza-Szegö and Redheffer. As an application, we prove a conjecture of Bennett.

math.FA↗
arXiv2008

A note on $l^p$ norms of weighted mean matrices

We present some results concerning the $l^p$ norms of weighted mean matrices. These results can be regarded as analogues to a result of Bennett concerning weighted Carleman's inequalities.

math.FA↗
arXiv2008

Topological wave functions and the 4D-5D lift

We revisit the holomorphic anomaly equations satisfied by the topological string amplitude from the perspective of the 4D-5D lift, in the context of ''magic'' N=2 supergravity theories. In particular, we interpret the Gopakumar-Vafa relation between 5D black hole degeneracies and the topological string amplitude as the result of a canonical transformation from 4D to 5D charges. Moreover we use the known Bekenstein-Hawking entropy of 5D black holes to constrain the asymptotic behavior of the topological wave function at finite topological coupling but large Kähler classes. In the process, some subtleties in the relation between 5D black hole degeneracies and the topological string amplitude are uncovered, but not resolved. Finally we extend these considerations to the putative one-parameter generalization of the topological string amplitude, and identify the canonical transformation as a Weyl reflection inside the 3D duality group.

hep-th↗
arXiv2008

$n$-level density of the low-lying zeros of quadratic Dirichlet $L$-functions

The Density Conjecture of Katz and Sarnak associates a classical compact group to each reasonable family of $L$-functions. Under the assumption of the Generalized Riemann Hypothesis, Rubinstein computed the $n$-level density of low-lying zeros for the family of quadratic Dirichlet $L$-functions in the case that the Fourier transform $\hat{f}(u)$ of any test function $f$ is supported in the region $\sum^n_{j=1}u_j < 1$ and showed that the result agrees with the Density Conjecture. In this paper, we improve Rubinstein's result on computing the $n$-level density for the Fourier transform $\hat{f}(u)$ being supported in the region $\sum^n_{j=1}u_j < 2$.

math.NT↗
arXiv2008

(Non)-supersymmetric Marginal Deformations from Twistor String Theory

The tree-level amplitudes in $β$-deformed theory are studied from twistor string theory. We first show that a simple generalization of the proposal in hep-th/0410122 gives the correct results for all of the tree-level amplitudes to the first order of the deformation parameter $β$. Then we give a proposal to all orders of $β$ and show this matches the field theory. We also show the prescription using connected instantons and the prescription using disconnected instantons are equivalent in the deformed twistor string theory. The tree-level amplitudes in non-supersymmetric $γ$-deformed theory are also obtained in this framework. The tree-level purely gluonic amplitudes in theories with generic marginal deformations are also discussed in the twistor string theory side.

hep-th↗
arXiv2007

Finite Sections of Weighted Hardy's Inequality

We study finite sections of weighted Hardy's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.

math.CA↗
arXiv2007

Electric-magnetic Duality and Deformations of Three-Dimensional CFT's

SL(2,Z) duality transformations in asymptotically AdS4 x S^7 act non-trivially on the three-dimensional SCFT of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point. We develop a systematic method to holographically obtain the deformations of the boundary CFT and show how electric-magnetic duality relates different deformations. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the RG flow relates S-dual CFT's. Correlation functions in the CFT are computed by varying magnetic bulk sources, whereas correlation functions in the dual CFT are computed by electric bulk sources. Under massive deformations, the boundary effective action is generically minimized by massive self-dual configurations of the U(1) gauge field. We show that a self-dual choice of boundary conditions exists, and it corresponds to the self-dual topologically massive gauge theory in 2+1 dimensions. Thus, self-duality in three dimensions can be understood as a consequence of electric-magnetic invariance in the bulk of AdS4.

hep-th↗
arXiv2007

A Note On Mixed Mean Inequalities

We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.

math.CA↗