Questions tagged [algebraic-geometry]

Use for questions about algebraic geometry as it applies to physics. Purely mathematical questions should NOT go here, instead, they belong on Math Stack Exchange.

2
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1answer
79 views

Doubt about mathematical construction underlying physical systems

Consider the first and second videos of this playlist $[1]$. It seems the professor tried to discuss some heuristic approach between number theory abstract algebra and physics; Classical Physics is ...
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0answers
12 views

For the torus to rotate 180 degrees around the East-West symmetry axis, what happens?

(Suppose to ignore the deformed friction and torus when rotating)
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0answers
30 views

Connectedness on Special Kaehler manifolds

I just wanted to make a short/concise question which is quite mathematical but the aim is physical so I would like to ask it here. Anyone knows if there is a general statement about connectedness on ...
0
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0answers
28 views

singularity blow up in supersymmetric theories

I have been doing some reading on algebraic geometry, in particular singularity resolutions. All the examples I am familiar with in physics correspond to singularities of the extra dimensions (e.g. ...
2
votes
1answer
226 views

Algebraic geometry and topology for string theory [duplicate]

I am looking for a comprehensive book or notes in algebraic geometry and topology techniques used in string theory compactifications covering topics like orientifolds, orbiolds, Calabi Yau manifolds ...
2
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0answers
51 views

Geometric interpretation of dimensional reduction of $E_8 \times E_8$ string

Following on from this question. I'm trying to get a geometric picture of what happens under dimensional reduction. Let me focus on a single $E_8$ factor, in 10 dimensions - the Lagrangian will ...
5
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0answers
194 views

Relation between Topological String Theory and Physical String Theory?

I'm familiar with topological string theory from the mathematical perspective. In my narrow world, the topological string partition function is given by the Gromov-Witten partition function, which is ...
1
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0answers
90 views

Intuition for curves of self-intersection in F-Theory

I'm trying to study some papers on F-Theory where the standard language of communication involves ideas and terminology from algebraic geometry, specifically intersection theory. As a concrete ...
1
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0answers
235 views

Why is important to know the geometry of the moduli space of vacua in a SUSY gauge theory?

I'm studying the moduli space of vacua for some supersymmetric gauge theory and I want to know specifically why it is important to know the geometry of this space. I know everything about the division ...
1
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0answers
69 views

Proving a geometric relation in 2D Minkowski spacetime [closed]

The triangle on the picture is the (future) causal domain of dependence of the interval of length $A$. The intervals of length $B$ and $C$ are relatively boosted to each other. How do I prove that $AD=...
1
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2answers
256 views

ADE Gauge Theory and String Theory

I should preface this my saying that I'm an algebraic geometer, and am not terribly knowledgeable about physics, nor the physics literature. I want to consider the singular surfaces $\mathbb{C}^{2}/...
2
votes
1answer
107 views

Connection between homotopic maps from $X\to Y$ and homotopic paths in $Y$ in the context of SU(2) Yang-Mills instantons

EDIT: I was reading little bit of homotopy theory in trying to understand the difference between homotopic maps from $X\to Y$ and homotopic paths in $Y$, and their significance in the context of SU(2) ...
4
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1answer
209 views

Relation between second cohomology and central extensions

In Blumenhagen's text on conformal field theory, after deriving the central extension of the Witt algebra, namely the Virasoro algebra, $$[L_m,L_n] = (m-n)L_{m+n} + \frac{c}{12}(m^3-m)\delta_{m+n,0}$...
4
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1answer
818 views

Relation between QFT and algebraic geometry

So, I've read this article who mentioned that physicists in LHC, while calculating the Feynman diagrams in one of their experiments, noticed a strange pattern: the numbers emerging from Feynman's ...
1
vote
1answer
80 views

How should I physically understand the slope stability of vector bundles on a manifold X?

Very basic question here as I try to come to grips with the geometry associated with string theory. I can (almost) understand how a manifold $X$ can admit or not admit a particular vector bundle on ...
1
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0answers
185 views

Applications of group theory in astronomy [closed]

I am familiar with applications of representation/group theory in terms of symmetries in quantum mechanics and general relativity, but what are some of their applications in astronomy? More ...
7
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2answers
165 views

Flavor symmetry fixes the Higgs branch in any 4D ${\cal N}=2$ QFT

Let us consider two different quantum field theories in 4 dimensional Minkowski spacetime, call them theory A and theory B, with 8 supercharges. (i.e. 4D $\mathcal{N}=2$ theories). Let $G_A$ be the ...
8
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0answers
166 views

Metric transformation, polygons and gravitons

I'm trying to understand the paper by Hitchin called: ''Polygons and gravitons". I'm stuck at page 471. At this point, he does some computations and obtains a metric: $$ \gamma dz d\bar{z}+\gamma^{...
2
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1answer
96 views

Simple question about holonomy and the orbifold $C^2/Z_{2}$

This query is from Gubser's TASI lectures on Special Holonomy in string theory and M-theory. There is a detailed description in the first lecture, of the orbifold $C^2/Z_2$ and I think I understand ...
3
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0answers
114 views

Reference for orbifolds in string- and M-theory

A number of orbifold constructions have been studied heavily in string- and M-theory over the years, establishing various dualities between different theories. Can someone point me to a slightly more ...
19
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1answer
2k views

Equation of a torus

In the recent paper http://arxiv.org/abs/1509.03612, page 37. They say that a torus can be described by the equation $$y^2=x(z-x)(1-x)$$ where $x$ is a coordinate on the base $\mathbb{P}_1$. Could ...
7
votes
1answer
688 views

How can I understand instantons as sheaves?

In specific, instantons are considered or interpeted as torsion free coherent sheaves. Why is that the case? Is there a nice way to understand this relation and of course also understand how the two ...
5
votes
1answer
231 views

What algebraic structure does the collection of all physical quantities form?

What algebraic structure -- by which I'm referring to abstract algebra theoretic ones such as ring, field, module, etc. -- does the collection of all physical quantities form? An related and/or ...
1
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0answers
170 views

Tropical Geometry and Quantization

Recently I saw this question posted on Math Overflow asking about the motivations behind tropical geometry. The OP mentions that tropical geometry can be viewed as the classical limit of regular ...
18
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0answers
746 views

TQFTs and Feynman motives

Questions Is a topological quantum field theory metrizable? Or else a TQFT coming from a subfactor? For a given metric, are there always renormalization and Feynman diagrams? Is there always a Feynman ...
3
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0answers
200 views

Estimating volume of moduli space of genus-g Riemann surface with n marked points

I wanted to know how can I estimate the volume of the moduli space of a Riemann surface of genus $g$ and having $n$ marked points. I am reading some old string theory papers which discuss divergences ...
5
votes
1answer
682 views

Which is the role of Algebraic Geometry in String Theory? [closed]

Could someone sketch me what algebraic geometry has to do with string theory? Are there other mathematical disciplines that are interwoven with string theory? I'm aware of a similar question on math....
3
votes
0answers
99 views

Is it possible to build up holography in a closed manifold, i.e., in a manifold with a mathematical boundary?

I was wondering about the AdS/CFT correspondence basics. It is constructed on the idea of conformal compactification, in which a open manifold $M$ is homeomorphic related to a closed one $N$ through a ...
6
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1answer
479 views

Etale bundles and sheaves

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or ...
14
votes
1answer
3k views

How algebraic geometry and motives appears in physics?

First, I'm not a physicist so I have just a little background in physics. I have been reading some noncommutative geometry books and papers (Connes, Rosenberg, Kontsevich etc) and a lot of high ...
3
votes
0answers
82 views

Spinors on algebraic plane curves

I'm interested in parameterizing spinors on Riemann surfaces. For my purposes, it's best to represent the Riemann surfaces as immersed in $\mathbb{C}P^2$, i.e. as algebraic plane curves. Apparently, ...
5
votes
2answers
613 views

Is there a physical motivation to study finite fields?

Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never ...
1
vote
1answer
290 views

transformations with commutators and anticommutators that generate displacements

is well known that composition of point reflections generate pure displacements. This implies that the commutator of two point reflections will be a pure displacement. Are there similar elemental ...
15
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1answer
641 views

What is Motivic mathematics and how is it used in physics?

In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being ...
24
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8answers
7k views

Crash course on algebraic geometry with view to applications in physics

Could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an ...