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.

35 questions
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Doubt about mathematical construction underlying physical systems

Consider the first and second videos of this playlist $$. It seems the professor tried to discuss some heuristic approach between number theory abstract algebra and physics; Classical Physics is ...
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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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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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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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) ...
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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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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....
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...