Aspects of dual models many years ago
E. Corrigan
应邀为文集撰稿：《弦论的诞生》，由Andrea Cappelli、Elena Castellani、Filippo Colomo和Paolo Di Vecchia编辑。
Invited contribution to the collection of articles: `The Birth of String Theory', edited by Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia.
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Simplicial and modular aspects of string dualities
这个博士本论文收集了现代统一理论两个不同方面的研究结果。在第一部分中，我总结了弦对偶的单纯性方面的研究成果。利用边界共形场论技术，我研究了随机Regge三角剖分和开弦论之间的耦合，讨论了它在规范/引力对应中的意义。第二部分报告了在hep-th/0309237论文中得到的结果，该论文致力于寻找超弦理论的宇宙学背景。
Aspects of Duality in N=2 String Vacua
我们收集进一步的证据之间的$N=2$杂种优势和II型弦真空在一个特定的模型建议Kachru和Vafa的建议的对偶性。在规范部门的前面的分析是扩展，它进一步表明，对偶性也适用于一圈引力耦合的向量多重态。
Thermofield Dynamics of the Closed Bosonic String - Physical Aspects of the Thermal Duality -
利用玻色热弦系综的热对偶对称性和模不变性的热稳定性以及整体相结构描述了D=26的封闭玻色热弦论的热场动力学.
Aspects of duality
本论文讨论了量子场论和弦论中对偶性的各个方面。在第一部分中，我们考虑拓扑量子场论中的对偶性，集中在Donaldson和Seiberg-Witten理论作为研究四维流形的（对偶）方法。这些理论的低维变体也进行了讨论。在论文的第二部分中，我们讨论了二维西格玛模型中的对偶性，通过研究由beta函数产生的重整化群流和T-对偶性之间的相互作用。本文提出的假设是，为了使它们相互一致，它们应该作为参数空间中的算子交换。论文的最后一部分通过回顾弦论中的一些非微扰对偶性，将这些问题带入透视。
Some Global Aspects of Duality is String Theory
我们探讨了弦论和场论中对偶变换的一些全局方面。我们详细分析了等价的对偶模型对应于不同的拓扑结构的水平上的配分函数和交换对偶的运营商对应。我们分析了宇宙学常数在这些变换下的行为。我们还探讨了几个例子，非阿贝尔对偶的经典背景解释可以保持原来的和对偶理论。特别地，我们构造了一个非阿贝尔对偶的$SL(2,R)$，它是一个三维的黑洞
Thermofield Dynamics of the Heterotic String - Physical Aspects of the Thermal Duality -
利用D = 10杂化热弦论的热对偶对称性和模不变性的热稳定性，结合D = 10杂化热弦系综的整体相结构，描述了D = 10杂化热弦论的热场动力学.
Aspects of Space-Time Dualities
本文研究四维流形上阿贝尔规范理论的对偶群及其二维化约。对偶群包括除了关联不同规范耦合矩阵之外还关联不同时空的元素。我们解释（一些）这样的对偶作为几何对称性的紧致化理论在更高的维度。特别是，我们考虑紧化的（自对偶）2-形式在6-D，和紧化的自对偶4-形式在10-D。讨论了它与6维自对偶超弦和IIB型超弦的关系。
In this paper we study aspects of geometries in Type IIA and Type IIB String theory and elaborate on their field theory dual pairs. The backgrounds are associated with reductions to Type IIA of solutions with $G_2$ holonomy in eleven dimensions. We classify these backgrounds according to their G-structure, perform a non-Abelian T-duality on them and find new Type IIB configurations presenting {\it dynamical} $SU(2)$-structure. We study some aspects of the associated field theories defined by these new backgrounds. Various technical details are clearly spelled out.
Aspects of Heterotic/M-Theory Duality in D=3
本文研究了Calabi-Yau四重上紧化的M-理论与Calabi-Yau三重上紧化的杂化弦的对偶性。我们的分析是基于在三个维度的低能量有效行动的比较。
Statistical Aspects of Neveu and Schwarz Dual Model
统计方法应用于Neveu和Schwartz模型，得到了重共振态的平均特征：自旋分布、衰变宽度等。考虑了由对易和反对易算符构成的双模型态谱的性质。在这种情况下，自旋特性与统计自举模型的结果一致。
Topological aspects of dual superconductors
我们讨论的拓扑方面的两个间隙超导体之间的约瑟夫森耦合和没有间隙。我们解决了非平凡的拓扑方面的双重超导体及其连接到迈斯纳效应和磁通量子化。从U（1）$\times$ U（1）规范群所对应的弦的Hopf不变量、曲率和挠率的角度讨论了拓扑纽结弦几何.
In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS_5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d N=2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Nunez. This suggests different completions of the long quiver describing the CFT dual to the non-Abelian T-dua…
Simplicial Aspects of String Dualities
我们将展示如何随机三角化的表面的研究合并的研究开/闭弦对偶。特别是我们将讨论共形场论，它出现在开弦部门及其影响。
Aspects of T-duality in Open Strings
利用正则变换方法研究了各种$D$ -流形中开弦的T-对偶性。我们表明，这种方法是特别有用的研究映射的边界条件，因为它提供了一个明确的初始和对偶变量之间的关系。我们考虑了非阿贝尔对偶变换，证明了在一定的限制条件下，对偶变换是一个弯曲的$(d-{\rm dim}G-1)$ D-膜，其中$d$是时空的维数，$G$是非阿贝尔对称群.推广到$N=1$超对称西格玛模型与阿贝尔和非阿贝尔等距也被认为是。
Regge amplitudes from AdS/CFT duality
很久以前，弦论就开始寻求对观测到的强相互作用振幅的高能“雷奇行为”的理论解释，但这个35年之久的难题仍然没有解决。我们将讨论如何现代工具，如广告/CFT对应给一个新的见解的问题。
Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
规范σ模型的论点，由T-对偶相关的弦背景给出等价的量子理论重新考虑，考虑到全球的考虑。拓扑上的障碍，以衡量西格玛模型引起的障碍，T-对偶，但这些都是温和的比那些衡量：它是可能的T-对偶一大类的西格玛模型，不能衡量。对于环面纤维化的背景，T-对偶可以在没有全局定义的Killing向量场的一般情况下应用于纤维化，因此没有可以测量的等距对称性; T-对偶的推导扩展到这种情况。T-对偶变换是用整体定义的量表示的。本文讨论了非几何弦背景的推广问题，分析了T-对偶背景为几何背景的条件和T-折叠的拓扑结构。
Geometrical Aspects of Fivebranes in Heterotic/F-Theory Duality in Four Dimensions
利用稳定退化的方法研究了Calabi-Yau三重空间上F-理论紧化与杂优紧化的对偶的Calabi-Yau四重空间的局部几何，其中五个膜包裹着三重空间中的全纯曲线.当五膜包裹相交的曲线时，或者当许多五膜包裹同一条曲线时，对偶四重以有趣的方式退化。我们发现，其中一些可以有效地描述在退化的基础上的椭圆纤维化的这些fourfolds。我们使用威滕的标准，以确定哪五个膜可以导致非微扰超势的产生。
We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of "spectator" fields in this process and also show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double. We then develop the N=(0,1) supersymmetric duality invariant formalism.
Aspects of Open-Closed Duality in a Background B-Field
研究背景$B$场中的闭弦交换.通过对玻色弦论中两点一圈振幅的分析，我们证明了最低弦模、快子模和无质量弦模的树能级交换具有与非对易规范理论中非平面扇形相似的红外奇异性。我们进一步隔离的贡献，从每个无质量模式。我们解释这些结果作为开/闭弦对偶的表现形式，其中边界非对易规范理论的IR行为是从闭弦的体理论重建的。
Twistors and Aspects of Integrability of self-dual SYM Theory
借助Penrose-Ward变换，将超扭量空间上的某些全纯向量丛与四维自对偶SYM理论的运动方程联系起来，我们构造了该理论的隐无穷维对称性.我们还提出了一个新的和更短的证明（参见。hep-th/0412163）的某些变形代数和隐对称代数之间的关系。本文是根据作者在2005年俄罗斯杜布纳BLTP超对称性和量子对称性研讨会上的讲话撰写的。
Some Thermodynamic Aspects of Pure Glue, Fuzzy Bags and Gauge/String Duality
本文用弦公式计算了无夸克SU（3）规范理论的热力学性质（1.2Tc < T <3Tc）。计算结果与点阵数据吻合较好。本文还对SU（N）规范理论作了评述。
We study quantum aspects of the galileon duality, especially in the case of a particular interacting galileon theory that is said to be dual to a free theory through the action of a simultaneous field and coordinate transformation. This would appear to map a theory with multiple vacua to one with a unique vacuum state. However, by regulating the duality transformation using external sources, we are able to preserve the full vacuum structure in the dual frame. By explicitly calculating the one-particle irreducible effective action on a maximally symmetric background, we identify a semi-classica…
The primary focus of this thesis is to investigate the mathematical and physical properties of spaces that are related by T-duality and its generalisations. In string theory, T-duality is a relationship between two a priori different string backgrounds which nevertheless behave identically from a physical point of view. These backgrounds can have different geometries, different fluxes, and even be topologically distinct manifolds. T-duality is a uniquely `stringy' phenomenon, since it does not occur in a theory of point particles, and together with other dualities has been incredibly useful in…
Aspects of Open-Closed Duality in a Background B-Field II
在[hep-th/0503009]中，在玻色子理论的背景下，由于在非对易规范理论的非平面图中积分出高动量模而产生的IR奇异项可以从低位树能级闭弦交换中恢复。这是世界单开闭弦对偶的自然结果。在这里，使用相同的设置，我们研究的现象，非对易${\cal N}=2$规范理论实现的$D_3$分数膜定位在固定点的$C^2/Z_2$。无质量闭弦交换的红外奇异性与单圈规范理论的红外奇异性完全相等。这是由于大量模式的所有贡献被抵消的结果。
Aspects of Duality and Confining Strings
在有效场论模型下，用孤子的形式考察了约束弦的激发能谱。谱可以用一个谱函数来表征，弦的扭曲和弯曲可以用这个谱函数在对偶变换下的不变性来表示。一般的考虑和数值模拟表明，谱函数可以近似为一个简单的合理的形式，我们建议成为准确的杨米尔斯理论。
On the Integrability Aspects of the Self Dual Membrane
精确的量子可积性方面的一个部门的膜进行了研究。结果发现，在平坦的目标时空背景中运动的球形膜承认与SU（infty）SDYM方程（维数减少到一个时间维）相关联的一类可积解。经过适当的分析，SDYM方程可以转化为连续的Toda分子方程，其对称代数是W（infty）+{ \bar W}（infty）代数的降维.后一个代数是显式构造的。最高权表示直接从W（\infty）代数的最高权态和Toda分子的量子态之间的无限数量的定义关系建立。离散状态也被构造。全（降维）量子SU（infty）YM理论仍有待探索。
A manifestly T-dual invariant formulation of bosonic string theory is discussed here. It can be obtained by making both the usual string compact coordinates and their duals explicitly appear, on the same footing, in the world-sheet action. A peculiarity of such a model is the loss of the local Lorentz invariance which is required to be recovered on-shell. This dictates a constraint on the backgrounds which characterizes the double geometry of the target space. Constant and non-constant backgrounds are considered. In the former case, the local Lorentz constraint implies the geometry of a double…
Aspects of self-dual Yang-Mills and self-dual gravity
本文研究了自对偶Yang-Mills理论与自对偶引力中的全同螺旋度圈振幅，提出了基于Berends-Giele流和有效传播子的任意多重数一圈振幅新公式，并探讨了其反常解释及与量子引力紫外发散的联系。
Is There a Stringy Description of Self-Dual Supergravity in 2+2 Dimensions?
众所周知的N=2弦论描述了自对偶引力，就像Ooguri和Vafa不久前所证明的那样。为了寻找这个理论的一个变体来描述2+2维中的自对偶超引力，我们构造了两个新的N=2弦理论，其中目标空间是一个超空间。这两种理论都包含无质量的标量场和旋量场，其中一种具有时空超对称性。然而，我们发现这些场的相互作用并不对应于自对偶超引力。在我们的构造中，我们使用了基本的（2，2）超空间变量，并考虑了这些变量中的二次约束。对于自对偶超引力的严格描述，可能需要一个更一般的结构。
Aspects of the Hypermultiplet Moduli Space in String Duality
一个在卡-丘三重上紧化的IIA型弦（或F-理论）被认为是一个在K3曲面乘以2-环面（或K3曲面）上的杂种弦的对偶。我们考虑如何得到超多重态的模空间是确定这两个图片之间的情况下，E8 xE 8杂种优势字符串。作为例子，我们讨论了K3曲面上的SU（2）-丛和G2-丛以及点状瞬子的情形。我们导致一个相当漂亮的识别之间的积分上同调的卡-丘三倍和一些积分结构的杂种优势的一面有点让人想起镜像对称。我们讨论了探测IIA型弦和杂化弦的非微扰效应的后果。
Aspects of Large N Gauge Theory Dynamics as Seen by String Theory
本文利用Maldacena的对偶结构探讨了大N超对称和非超对称规范理论的一些特征。我们将证明，由此产生的规范理论的强耦合行为与我们对这些理论的定性预期是一致的。其中一些一致性检查是非常重要的，并提供了额外的证据的有效性提出的对偶。
String duals of two-dimensional (4,4) supersymmetric gauge theories
本文研究了N=（4，4）超对称的二维场论。弦背景再现了对偶场论的某些非微扰方面，具有大量的颜色N_c和可调数量的味道N_f。不同方面的二维场论进行了讨论，其中包括规范耦合的运行，在希格斯和库仑分支，纠缠熵和我们的弦背景的非相对论版本的介子的频谱。
Supersymmetry and flavor in a sugra dual of N=1 Yang-Mills
在弦论中引入D-膜，可以全息地处理场论的某些方面。在这项工作中，我们研究这个问题的框架内的对偶N=1 YM，所谓的Maldacena-Nunez模型。发现了D5-膜探测的超对称嵌入，并将其解释为规范理论的基本味的增加。这允许给出N=1 SQCD的一些已知方面的双重描述，并计算介子的质谱。
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of …
About twelve years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of $QCD$. This non-perturbative phenomenon is dubbed Effective Locality. In a much simpler way than in $QCD$, the most remarkable and intriguing aspects of Effective Locality are presented here, in the Yang--Mills theory on Minkowski spacetime.
On algebraic geometric and computer algebra aspects of mirror symmetry
我们综述了弦论中镜像对称和对偶性的一些代数几何方面。简要回顾了计算机代数在代数几何和弦论中的一些应用。
To study thermal aspects of the ABJM theory in the strongly coupled regime, we carry out the CP3 invariant dimensional reduction of the type IIA supergravity down to four dimensions. We then investigate zero and finite temperature responses of the operators which are dual to the AdS scalar and vector fields. Two scalar operators are shown to have finite-temperature condensations by coupling of constant source term. The currents dual to the massless and massive gauge fields are not induced by coupling of constant boundary vector potential, which implies that the phase described by black brane b…
Aspects of WZW models at critical level
我们考虑临界水平（等于对偶Coxeter数）的非紧WZW模型作为弦论中引力背景的无张力极限。重点讨论了k=2时的欧氏黑洞陪集SL（2，R）_k/U（1）。在这个极限下，引力场以具有无限背景电荷的刘维尔场的形式出现，模型的世界面对称性变成了没有Virasoro生成元的W_ \infty的截断形式。这被认为是SL（2，R）k流代数的Langlands对偶性的表现，它在两个极端极限处的能级值与大值相关。然而，SL（2，R）_k/U（1）陪集模型在自对偶值k=3以下的物理解释仍然是难以捉摸的，包括k=2时的非共形理论。
About ten years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of QCD and dubbed Effective Locality. This feature of QCD is nonperturbative as it results from a full gauge invariant integration of the gluonic degrees of freedom. In this review article, a few salient theoretical aspects and phenomenological applications of this property are summarized.
Perturbative and non-perturbative aspects of pure N=1 super Yang-Mills theory from wrapped branes
的Maldacena-Nunez解决方案是广义的，包括一些积分常数，其中之一控制的分辨率的奇异性的包装D5膜背景。本文计算了纯N=1超Yang-Mills（SYM）理论的一些性质，其中包括胶子凝聚、规范耦合的β函数和与Veneziano-Yankielowicz有效势有关的膜探测势.每个积分常数在对偶SYM理论中具有精确的含义，例如，由重力配置捕获的非微扰SYM物理量由奇点分辨率参数描述。
Some solutions describing vacuum decay exhibit a catastrophic instability. This, so-called negative mode problem in quantum tunneling with gravity, was discovered 34 years ago and in spite of the fact that in these years many different groups worked on this topic, it has still not been resolved. Here, we briefly summarize the current status of the problem and investigate properties of the bounces, numerically and analytically for physically interesting potentials. In the framework of the Hamiltonian approach we show that for generic polynomial potentials the negative mode problem could arise a…
We study the moduli space of self-dual instantons on $\mathbb{C}P^2$. These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact directions. In this paper we probe these, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover, the ADHM-like construction can be embedded into a $3d$ gauge theory with a known gravity dual. Using this, we realize in $AdS_4/CFT_3$ (part of) the instanton moduli space providing at the same time further evidence suppor…
The double copy is by now a firmly-established correspondence between amplitudes and classical solutions in biadjoint scalar, gauge and gravity theories. To date, no strongly coupled examples of the double copy in four dimensions have been found, and previous attempts based on exact non-linear solutions of biadjoint theory in Lorentzian signature have failed. In this paper, we instead look for biadjoint solutions in Euclidean signature, which may be relatable to Yang-Mills or gravitational instantons. We show that spherically symmetric power-like Euclidean solutions do not exist in precisely f…
Soliton equations in N-dimensions as exact reductions of Self-Dual Yang-Mills equation IV. The mM-LXII and Bogomolny equations
多维孤子几何的一些方面被认为是。讨论了2+1维孤子方程与自对偶Yang-Mills方程和Bogomolny方程之间的关系。
Soliton equations in N-dimensions as exact reductions of the Self-Dual Yang-Mills equation V. Simplest (2+1)-dimensional soliton equations
多维孤子几何的一些方面被认为是。证明了某些简单的（2+1）维方程是自对偶Yang-Mills方程或其高阶方程的精确约化。
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