Questions tagged [moduli]
The moduli tag has no usage guidance.
63 questions
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Modified Special Geometry of SUSY Moduli Space
It is known that the Coulomb branches of 5d $\mathcal{N}=1$ and 4d $\mathcal{N}=2$
SUSY (both have eight supercharges) satisfy special geometry. This means that there exists a holomorphic prepotential ...
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Distance conjecture being false in $\phi^4$ theory
One part of Distance conjecture states that free theory (Higher spin) are at infinite distance away from any arbitrary point on conformal manifold where the distance is measured with respect to ...
- 3,063
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Do singular $G_2$-holonomy manifolds in M-theory have stable compactifications?
In this paper: Chiral Fermions from Manifolds of G2 Holonomy it is shown that compactifications of M-theory on a $7d$ $G_2$-holonomy manifold $X$, generate chiral fermions, if only $X$ is singular.
I ...
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Why should bulk modulus always be positive?
The minus sign that appears in Equation 12.39 is for consistency, to ensure that $B$ is a positive quantity. Note that the minus sign ($–$) is necessary because an increase $\Delta p$ in pressure (a ...
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Why don't the extra compact dimensions collapse on themselves?
Why are the extra compact dimensions stable and do not collapse?
I know the anomaly cancellation is the reason why the extra dimensions are necessary.
But I can not visulize how the anomaly ...
- 1,280
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Dimension of moduli space for SQCD
We are in $\mathcal{N}=1$ SUSY. Consider massless SQCD with gauge group $SU(N)$ and $F$ flavours. The quarks superfields $Q$ and $\tilde{Q}$ are $F\times N$ and $N\times F$ matrices respectively and ...
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Parametrization of classical moduli space for SUSY QED
A bit of context
I'm following Bertolini's notes on SUSY and in section 5.3.1 he claims that, for a SUSY theory without superpotential, i.e. in which the $D$-flat directions coincides with the moduli ...
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String Compactification on a Circle Results in a Moduli Space?
I have been reviewing some string theory for a project I'm working on and I have some questions regarding string compactifications on a circle and the precise definition/origin of the moduli space ...
- 82
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Why is bulk modulus large for a nearly Incompresible material?
Source of the picture
I don't understand why do we consider a large value of bulk modulus when we want to model incompressibe material? I mean bulk modulus is the bulk change in volume and the ...
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Moduli space for Riemann surfaces with boundaries and open string loop diagrams
I'm searching for information on the moduli space for Riemann surfaces with boundaries, like the ones used to compute open string loop diagrams. I found a huge lot of info for the case without ...
- 1,176
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Vacuum manifold and fermion condensation
Vacuum manifold is just another name for the manifold spanned by the ground states of quantum field theory. It is also called moduli space.
According to https://en.wikipedia.org/wiki/Vacuum_manifold, ...
- 4,376
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Vacuum manifold and moduli space
Vacuum manifold is just another name for the manifold spanned by the ground states of quantum field theory. It is also called moduli space.
According to https://en.wikipedia.org/wiki/Vacuum_manifold, ...
- 4,376
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Difference between moduli spaces of supersymmetric vs non-supersymmetric theories?
I have a basic conceptual question regarding the difference between moduli spaces in supersymmetric vs non-supersymmetric theories.
In usual non-supersymmetric theories, the existence of flat ...
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Stress to make concrete stronger
In reinforced concrete steel rods are embedded in wet cement and held in tension while the mixture dries. Once fully dry the tension is removed, and the concrete should be stronger as a result of this ...
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Target space of boundary CFT dual to a bulk string theory ($AdS_3/CFT_2$)
I was reading the Maldacena Ooguri paper where they mention that for the string theory living on $AdS_3\times S_3 \times M_4$ (where $M_4$ is $K3$ or $T^4$), the boundary CFT is the supersymmetric ...
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Is there a relationship between the complex modulus and the dynamic viscosity?
I have a material for which I know both the tensile storage modulus $E'$, and loss modulus $E''$ at a frequency of 1 Hz. As I understand it, $E'$ conceptually describes the elastic properties of the ...
- 1,394
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Which can support more weight, one thick rope or many thinner ropes?
Given the same total amount of material used and the same length of an individual rope, will many thinner ropes support more weight (withstand more tension) than one thick rope?
user255633
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Holomorphic 3-form on Calabi-Yau compactifications
What is the natural scale of the holomorphic 3-form on a Calabi-Yau?
$\Omega=\frac{1}{3!}\Omega_{abc} ~ dz^a\wedge dz^b \wedge dz^c$
$||\Omega||^2 = \frac{1}{3!}\Omega_{abc}\bar{\Omega}^{abc}$
...
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How does stretching of a coil involves shearing stress?
My book has this true/false question
$$\pmb {Question}$$
The stretching of a coil is determined by its sheer modulus.
$$\pmb {Answer}$$
True
But I am not able to comprehend as how does ...
user238497
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Why is shear modulus also known as modulus of rigidity?
The book I am referring to states the following -
The ratio of shearing stress to the corresponding shearing strain is
called shear modulus of the material and is represented by G. It is
also ...
- 127
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208
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What exactly do the zero-modes of the instanton mean?
I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
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Describing Calabi–Yau 3-fold
Background:
In Calabi-Yau 3-fold, the Kähler metric is given in terms of the Kähler potential $\kappa$ :
$ g_{i\bar{j}} = \partial_i \partial_{\bar{j}} \kappa$,
where $i, \bar{j}$ = 1,2,3 $ ( the ...
- 405
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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 ...
- 201
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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 ...
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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^{...
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Complexified Kahler moduli
The fundamental domain of the complex moduli of a torus can be identified to the upper half plane up to $SL(2,Z)$ transformations $\mathbb{H}/{SL(2,\mathbb{Z})}$, but I don't know why the complexified ...
- 49
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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 ...
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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?
user138802
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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,...
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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 ...
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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 ...
user151266
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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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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 ...
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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 ...
- 2,121
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $A$ ...
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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 ...
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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 ...
- 3,662
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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 ...
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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 ...
- 3,997
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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 ...
- 3,662
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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
...
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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 ...
- 3,662
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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 " ...
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