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Questions tagged [moduli]

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0
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1answer
34 views

Transverse and Longitudinal waves in a wire

The question is : The speed of longitudinal wave is ten times the speed of transverse waves in a tight brass wire. If the Young's Modulus of the wire is Y, then strain in the wire is? I have read ...
1
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0answers
21 views

Checking modularity-like transformation property

Assume $M$ is a 4 manifold. Let $Z_v$ be partition function of fixed magnetic flux $v$ with all instanton configuration summed over where $v\in H^2(M,Z/nZ)$. $\tau$ denotes complex parameter on upper ...
3
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1answer
90 views

Questions about the landscape in string theory

If I understand correctly, the string theory landscape is the totality of possible Calabi-Yau manifolds to make up the compact factor of space in string theory, in which there are of the order of $10^{...
0
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0answers
39 views

Moduli space of mirror theories in 3d upon susy breaking

First, maybe some quick exposition would be helpful. In the original work on 3d mirror symmetry, by Intriligator and Seiberg, they first define a $3d$ $\mathcal{N}=4$ gauge theory, whose moduli ...
1
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0answers
98 views

Complexified Kahler moduli

Fundamental domain of complex moduli of a torus can be identified to upper half plane up to $SL(2,Z)$ transformations $\frac{H}{SL(2,Z)}$, but I don't know why complexified Kaher moduli in string ...
3
votes
1answer
132 views

Shouldn't the frequency of a tuning fork depend on its shear modulus?

I know that the frequency of a tuning fork depends on its Young's modulus, but intuitively, shouldn't the frequency of a tuning fork depend on it's shear modulus, not it's Young's modulus, as the ...
0
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1answer
66 views

Would gravitons be massless particles associated to moduli fields in string theory?

String theory does predict massless particles associated with moduli fields that haven't been observed. Would gravitons be one of these particles?
3
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0answers
118 views

Are Instantons Quantum or Classical?

I'm talking specifically about instantons on four-manifolds, but my confusion here is probably of a more general nature. So I'd also appreciate less specific answers! Okay, so I know that in physics,...
1
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0answers
90 views

Relation between the momentum map and D-terms

Can someone explain to me the relation between the momentum map linked to symplectic quotients and the D-terms of a scalar potential for a $\mathcal{N}\geq 2$ supersymmetric gauge theory? I am ...
2
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1answer
363 views

Higgs and Coulomb Branches. What are they?

On Wikipedia, there is an article on Moduli(Physics). The link is the following https://en.wikipedia.org/wiki/Moduli_(physics) . What captures me is Higgs and Coulomb Branch. If you click the links on ...
1
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0answers
234 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 ...
0
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1answer
424 views

Relationship between Young's moduli and “mixed” Shear modulus in transversely isotropic materials

In isotropic elastic materials, the shear modulus, G, and the Young's modulus, E, are related via $$ G = \frac{E}{2 (1 + \nu)} $$ where $\nu$ is the Poisson ratio. As a consequence, as long as $\nu ...
8
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2answers
675 views

Is the partition function of non-conformal theories on a torus modular invariant?

Usually we say that the partition function of CFTs on a torus is modular invariant, because we define theory on a torus. If I have a non-conformal field the theory on a torus, is its partition ...
4
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0answers
90 views

Flux compactifications and the scalar potential

Does the scalar potential: $$V=e^K(K^{I \bar{J}})D_IW D_{\bar{J}}\bar{W}-3|W|^2$$ where $K$ is the Kähler potential and $W$ the superpotential, $D=\partial_I+\partial_IK$ and $I$ runs over all the ...
2
votes
1answer
337 views

Moduli spaces of supersymmetric field theories and their singularities

I'm a mathematician doing some work which is related to $\mathcal N=2$ supersymmetric quantum field theory in $d=4$ and am a little confused about the physical notion of moduli space in this context. ...
7
votes
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 ...
2
votes
1answer
452 views

Moduli space of torus compactifications

I am trying to understand some general statements made in the lecture notes by Vafa entitled "Lectures on Strings and Dualities" concerning toroidal compactifications (arXiv:hep-th/9702201). Question ...
3
votes
2answers
103 views

Question about notation used in writing the moduli space in string theory

In physics papers, particularly those by Aspinwall, or textbooks, I encounter things like $$\mathcal{M} \simeq O(\Gamma_{4,20})\setminus O(4,20)/((O(4)\times O(20))$$ For instance, this is from ...
7
votes
1answer
682 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 ...
3
votes
1answer
130 views

Question regarding moduli space of a Calabi-Yau manifold

On page 132 of "Introduction to Supergravity" by Horiatiu Nastase, the author says: On $M = CY_3$ (Calabi-Yau space) there are $b_3$ topologically nontrivial 3-surfaces, for which we can define a ...
3
votes
2answers
152 views

Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?

In these notes by Vafa on topological string theory he says in page 7 that the moduli of the 2-torus can be repackaged into two quantities: $$A=iR_1/R_2 \,\,\,\,\,\,\,\,\, \tau=iR_2/R_1$$ where $A$ ...
0
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0answers
139 views

Kähler Potential of Calabi-Yau volume

At tree level, the Kähler potential is given by (neglecting complex structure) $K = -\ln(-\mathrm{i}(\tau - \bar{\tau})) - 2\ln(V_{CY})$ where $V_{CY} = \frac{1}{6} \kappa_{abc}t^at^bt^c$ ia the the ...
0
votes
1answer
234 views

Why 5D gauge theory is non-renormalizable?

My question is following "Why 5D gauge theory is non-renormalizable?" Here I treat $5D$ supersymmetric gauge theories. Also I heard Non-renormalizablity of $5D$ gauge theories implies the ...
1
vote
0answers
93 views

Tadpole-free condition

Tadpole-free is a very important condition for perturbative string theory (which is equivalent to the theory to be expanded around the "right" vacuum). For simplicity, let's consider closed string ...
8
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0answers
1k views

Coulomb Branch vs. Higgs Branch (and the connection with D-branes, AdS/CFT)

I am confused about the difference between the Coulomb and Higgs branches of the moduli space of supersymmetric gauge theories. It's easy to find a definition for $D=4$, $\mathcal{N}=2$ supersymmetric ...
4
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0answers
83 views

Moduli space for $CP^N$ and $T^{*} CP^N$ in $\mathcal{N}=2$ SUSY

For complex $\phi$ in $U(1)$ gauge theory, \begin{align} |\phi_1|^2 + |\phi_2|^2 +\cdots |\phi_N|^2 =r \end{align} This equation $|\phi|^2=r$, describes sphere $S^{2N-1}$. Dividing the space of this ...
2
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0answers
124 views

Positivity of Bulk modulus and shear modulus in isotropic materials

I have been searching through many resources, but could not find a proper thermodynamic reasoning for why bulk and shear moduli for isotropic materials should be positive. Some resources like eFunda ...
0
votes
1answer
734 views

Higgs branch and Coulomb branch

I heard that the distinguish between Higgs branch and Coulomb branch is the limit of some parameters. (If i remember correctly, something like FI parameters. ) Here i want to know what is FI ...
0
votes
1answer
111 views

Why does product of Moduli and Diff x Weyl Variation vanish?

According to equation 5.2.5 in Polchinski :- $$\int d^2 \sigma~ \delta^{'}g_{ab} \times [-2(P_1 \delta \sigma)_{ab} +(2\delta w - \Delta \cdot \delta \sigma)g^{ab}]=0$$ The assumption here is that " ...
2
votes
1answer
287 views

Calabi-Yau condition, moduli and Lichnerowicz equation

I have a conceptual confusion about the metric moduli of Calabi-Yau manifolds, when I was reading Calabi-Yau compactification. As I understand, the metric moduli is parametrized by infinitesimal ...
6
votes
1answer
551 views

What's the Coulomb Branch and why is it important?

I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the ...
2
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0answers
230 views

High Young's Modulus and Tensile Strength of Carbon Nanotubes

I was recently reading about Carbon Nanotubes having extremely high Young's moduli, as well as high Tensile Strength, making them very interesting fibers. However, when I read this I wondered what was ...
9
votes
1answer
2k views

What is the Moduli Space, and why do we care about it?

What is the moduli space of a QFT? What does it mean exactly that there are different inequivalent vacua? Can someone give a precise definition of the moduli space, and some easy examples? And why ...
2
votes
0answers
57 views

Moduli potential in Type IIB String Theory

In the book String Theory and M-Theory by K. Becker, M. Becker and J.H. Schwarz: Why is the potential for moduli given by eq (10.168): $$\tag{10.168 }V(T,K) ~=~ \frac1{4\mathcal{V}^3} \Big( \int_{...
8
votes
1answer
415 views

What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

When reading about Higgs and Coulomb 'phases' I came across two separate definitions: The first tells us that the Higgs/Coulomb phases are determined by the representation that the Higgs field ...
6
votes
1answer
251 views

Background Gauge Condition In Moduli Space

I'm really confused on the background gauge condition for the moduli space of BPS-monopoles: \begin{equation} D_i \delta A_i + e [\phi , \delta \phi]=0 \end{equation} I can see that this conditions ...
3
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0answers
60 views

Linear combination of anomalous dimensions in effective potential on pseudomoduli space

In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3). In this equation, ...
6
votes
1answer
174 views

Disappearance of moduli for condensate of open strings

Consider a Dp-brane. Compactify $d$ spatial dimensions over a torus $T^d$. Suppose $d\geqslant p$, and that the Dp-brane is completely wrapped around the compactified dimensions. Look at the open ...
9
votes
1answer
612 views

precise definition of “moduli space”

I'm curious what the precise definition of the moduli space of a QFT is. One often talks about the classical moduli space, which then can get quantum corrections. Does this mean the quantum moduli ...
6
votes
1answer
200 views

Poisson structure on moduli space of CFTs

The moduli space of CFTs with central charge 26 forms the classical phase space of bosonic string theory, in some sense. Similarily the moduli space of SCFTs with central charge 10 forms the classical ...
18
votes
1answer
231 views

Instanton Moduli Space with a Surface Operator

I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator. Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are ...