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Supersymmetric Gauge Theory and Enumerative Geometry

超对称规范理论与枚举几何

基本信息

批准号：
EP/T004746/1
负责人：
Mathew Bullimore
金额：
$ 93.98万
依托单位：
Durham University
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2019
资助国家：
英国
起止时间：
2019 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FT004746%2F1
关键词：
Supersymmetric Gauge Theory Enumerative Geometry

项目摘要

Quantum field theory is the fundamental framework used by physicists to describe the world around us. It is spectacularly successful in describing a diverse range of phenomena, from the standard model of elementary particle physics to exotic phases of matter. In theories of weakly interacting particles, the outcomes of experiments such as the scattering and decay of particles can be predicted with astounding accuracy. A stunning example is the quantum theory of the electromagnetic field, where the theoretical prediction for the magnetic dipole moment of the electron agrees with experiment to more than 10 significant figures. However, there are many strongly interacting systems in nature, such as the strong nuclear force, where such calculations are not valid. Moreover, there are fascinating and important quantum mechanical phenomenon that only occur in strongly interacting systems. Therefore, despite the remarkable experimental success of quantum field theory, many fundamental questions remain to be understood. As in many other areas of science and mathematics, when faced with a seemingly insurmountable problem, it is useful to study simple examples that are both solvable and exhibit the phenomenon of interest. Supersymmetry plays this role in quantum field theory and has provided tremendous insight into strongly interacting systems. Furthermore, supersymmetric quantum field theories have deep connections to pure mathematics and the cross-fertilisation of ideas between these disciplines has been extremely fruitful. Discovering the underlying reason for this connection is surely an important step on the road to a full understanding of quantum field theory. My research lies at the interface of supersymmetric quantum field theory and an area of mathematics known as enumerative geometry. The basic idea of enumerative geometry is to count the number of solutions to geometric problems, such as how many lines intersect two points in a plane. This is just the beginning of a vast and fascinating area of mathematical research where the notion of `counting' takes on ever more sophisticated forms and incorporates the symmetries of geometric problems. It turns out that enumerative geometry appears in profound and surprising ways in supersymmetric quantum field theories. The interaction between these disciplines is beneficial in both directions. On one hand, insight from supersymmetric quantum field theory has the potential to generate new conjectures and computational techniques in mathematics that might otherwise lay undiscovered. On the other, mathematics allows us to refine our physical understanding by distilling the underlying physical principles into precise mathematical statements.

量子场论是物理学家用来描述我们周围世界的基本框架。从基本粒子物理的标准模型到物质的奇异相，它在描述一系列不同的现象方面取得了惊人的成功。在弱相互作用粒子理论中，粒子的散射和衰变等实验结果可以惊人的准确地预测出来。一个令人惊叹的例子是电磁场的量子理论，其中对电子磁偶极矩的理论预测与实验符合超过10个重要数字。然而，自然界中有许多强相互作用的系统，例如强核力，在这些系统中，这样的计算是无效的。此外，还有一些有趣而重要的量子力学现象，这些现象只出现在强相互作用的系统中。因此，尽管量子场论在实验上取得了显著的成功，但仍有许多基本问题有待理解。就像在科学和数学的许多其他领域一样，当面临一个看似无法克服的问题时，研究既可解又能表现出有趣现象的简单例子是有用的。超对称性在量子场论中扮演着这一角色，并为强相互作用系统提供了巨大的洞察力。此外，超对称量子场论与纯数学有着深厚的联系，这些学科之间的思想交叉交流取得了极大的成果。发现这种联系的根本原因，无疑是在全面理解量子场论的道路上迈出的重要一步。我的研究位于超对称量子场论和一个被称为计数几何的数学领域的交界处。枚举几何的基本思想是计算几何问题的解的数目，例如平面上有多少直线与两点相交。这只是一个广阔而迷人的数学研究领域的开始，在这个领域中，‘计数’的概念呈现出越来越复杂的形式，并纳入了几何问题的对称性。事实证明，在超对称量子场论中，列举几何以一种深刻而令人惊讶的方式出现。这些学科之间的互动在两个方向上都是有益的。一方面，来自超对称量子场论的洞见有可能在数学中产生新的猜想和计算技术，否则这些猜想和计算技术可能会被发现。另一方面，数学允许我们通过将潜在的物理原理提炼成精确的数学陈述来精炼我们对物理的理解。

项目成果

期刊论文数量（10）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

3d $mathcal{N}=4$ 椭圆曲线上的规范理论

DOI：
10.21468/scipostphys.13.1.005
发表时间：
2022
期刊：
SciPost Physics
影响因子：
5.5
作者：
Bullimore M
通讯作者：
Bullimore M

Generalized Symmetries and Anomalies of 3d N=4 SCFTs

3d N=4 SCFT 的广义对称性和反常性

DOI：
发表时间：
期刊：
影响因子：
0
作者：
Bhardwaj Lakshya
通讯作者：
Bhardwaj Lakshya

Twisted indices of 3d $$ \mathcal{N} $$ = 4 gauge theories and enumerative geometry of quasi-maps

3d $$ mathcal{N} $$ 的扭曲索引 = 4 个规范理论和准映射的枚举几何

DOI：
10.1007/jhep07(2019)014
发表时间：
2019
期刊：
Journal of High Energy Physics
影响因子：
5.4
作者：
Bullimore M
通讯作者：
Bullimore M

Non-invertible Symmetries and Higher Representation Theory I

不可逆对称性和更高表示理论 I

DOI：
发表时间：
期刊：
影响因子：
0
作者：
Bartsch Thomas
通讯作者：
Bartsch Thomas

Secondary Products in Supersymmetric Field Theory

超对称场论中的二次积

DOI：
10.1007/s00023-020-00888-3
发表时间：
2020
期刊：
Annales Henri Poincaré
影响因子：
0
作者：
Beem, Christopher;Ben-Zvi, David;Bullimore, Mathew;Dimofte, Tudor;Neitzke, Andrew
通讯作者：
Neitzke, Andrew