A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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What exactly is the “diagonal embedding” in the supersymmetric topological twist?

Consider $\mathcal{N}=2$ pure SYM theory. If we want to put the theory in a 4-manifold we take its topological twist. The global symmetry group $$G= SU(2)_{+} \times SU(2)_{-} \times SU(2)_I \times ...
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2answers
98 views

ΧΕΝΟΝ1Τ: Will it fail to discover DM? Why is it necessary? What benefits for society?

Since a new experiment (ΧΕΝΟΝ1Τ) will take place in Italy to directly detect WIMPs and since there are already many experiments trying to do the same or something similar (e.g. CERN LHC, LUX, CoGent, ...
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1answer
49 views

Matching bosonic and fermionic degrees of freedom in Wess-Zumino Lagrangian

In Wess-Zumino model, supersymmetric Lagrangian in addition to the ordinary complex scalar field $\phi$ contains auxiliary field $F$ (also complex scalar) to match the degrees of freedom of the Weyl ...
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1answer
201 views

Supersymmetric Sigma Model

I was working through the Mirror Symmetry book by Clay Math Institute. It deals with supersymmetric sigma model in 10.4 section. It doesn't derive how the action is invariant under the variation. I am ...
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218 views

Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
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99 views

Off-shell degrees of freedom of a massive vector field [closed]

A gauge boson is described by a vetor field $A_{\mu}$, so in four dimensions $\mu$ runs from $0$ to $4$ and thus $A_{\mu}$ has $4$ degrees of freedom (d.o.f), but the gauge invariance ...
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1answer
89 views

What does it mean for an action to be defined “on-shell”?

Some actions like 11D supergravity are defined "on-shell". What does this mean exactly? Can you give me an example? Say for example the Klein-Gordon action. Can this be defined on-shell too?
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Construction of $\mathcal O(-1) \oplus \mathcal O(-1)$ over $CP^1$ [closed]

First, Consider a $\phi$ as a coordinates on a copy of $Z= C^N$ Then, I know \begin{align} |\phi_1|^2 + |\phi_2|^2 + \cdots |\phi_N|^2 = r \end{align} which describe $S^{2N-1}$. Implementing $U(1)$ ...
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35 views

Supersymmetry breaking and normalizable zero modes

Why does supersymmetry always lead to normalizable zero modes? For example, it is stated in the paper by Michelson and Kaplan (http://arxiv.org/abs/hep-th/9510053) that we can assume, without loss of ...
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80 views

Jim Gates' discovery of error-correcting codes in equations of supersymmetry

Can anyone explain what's going on here, in a way that isn't just a lot of gee-whiz? Here's the arXiv article. I'm more of a computer science person than a physicist, so error-correcting codes are ...
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35 views

Chiral multiplet : Fundamental and adjoint representation and its Lagrangian

In supersymmetry theory, consider $4d$ $N=1$ theory, we know that chiral superfield (In fundamental representation $\Phi \rightarrow e^{i\alpha} \Phi$) $\Phi$ and its lagrangian is given as ...
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260 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
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128 views

Intuition behind Nekreasov's instanton partition function. What do the partitions represent exactly?

I am struggling to understand many things behind Nekrasov's solution. Firstly I want to understand the following In this theory, $a$ represents VEVs the Higgs scalar. So, is the gauge field of the ...
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37 views

M-theory compactified on $S^4$

I am trying to understand what happens to the 32 supersymmetries of M-theory when it is compactified on $S^4$, with the other seven dimensions being flat, e.g., $\mathbb{R^7}$, $\mathbb{R^6} \times ...
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9 views

How can we reduce the number of necessary parameter to 19 in phenomenological Minimal Supersymmetric Standard Model (pMSSM)?

I am very new in SUSY and I heard something about pMSSM. Question is that how we can reduce the number of necessary parameter to 19 in pMSSM. If you have any suggestion as a brief introduction or any ...
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41 views

What is the importance of $2d$ supersymmetric gauge theory? [closed]

I have been working $2d$ $N=(2,2)$ theories focused on checking duality like, Seiberg duality (2d version: named "Hori-Tong" duality) and its extension. During the study i got $2d$ $N=(2,2)$ ...
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1answer
36 views

Question about Supermatrix algebra

This question is inspired from a reading of Appendix F of P. van Nieuwenhuizen, Supergravity, Phys. Rep. 68 (1981) pp. 369-374. Consider a "supermatrix" $$M = \left(\begin{array}{cc} A & B\\ C ...
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48 views

M5 brane zero modes

The Euclidean M5 brane worldvolume has an anti self-dual 3-form and two negative chirality spinors. The spinors can couple to the SO(5) gauge fields of the normal bundle, but the 3-form cannot couple ...
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28 views

Lagrangian for $\mathcal{N}=4$ SQED in 3D

What is the Lagrangian for $3D$ $\mathcal{N}=4$ supersymmetric QED, with $N_f$ hypermultiplets? In particular, which is the form of the Fayet-Iliopulos terms, and the real mass terms?
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96 views

Pole in reflection/transmission coefficient and bound states

I was working on a scattering problem in a quantum mechanical system with Hamiltonian $$H_1=A^{\dagger}A=(-\partial_x+W(x))((\partial_x+W(x))).$$ One can show that a 'supersymmetric' partner to this ...
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28 views

N=4 d=3 susy algebra

Does anybody know how to derive the $\mathcal{N}=4$ d=3 susy algebra doing a dimensional reduction from the most famous $\mathcal{N}=4$ d=4? Equivalently, does it exist a reference in the literature ...
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28 views

The BPS mass formula for 3d N=4

Is the mass formula (or equivalently the central charge formula) known for BPS particles in 3d $\mathcal{N}=4$ susy gauge theories? In particular, what is its dependence on the Fayet-Iliopoulos ...
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1answer
132 views

Equation of motion of an auxiliary field

I'm a newbie in the field of QFT and SUSY, so I'm warning you: this might be a stupid question. I'm working with auxiliary fields to describe supersymmetric models and I understand that upon ...
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1answer
64 views

Meaning of Supersymmetry

Supersymmetry is a relation between bosons and fermions. Based on this definition, what is the meaning of "number of supersymmetries"?
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33 views

What are the global symmetries of $\mathcal{N}=2$ SYM before twisting and after twisting?

I am confused with the global symmetries of $\mathcal{N}=2$ SYM. On one hand I know that the theory has a $U(2)_R = SU(2)_R \times U(1)_R$ symmetry. Now, there exists also a $U(1)_B$ global symmetry. ...
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1answer
278 views

Hermitian conjugate of spinors

In any textbook, hermitian conjugate of spinor is defined like $ \psi_{\alpha}^{+}=\bar\psi_{\dot{\alpha}} $ and $(\psi^{\alpha})^{+}=\bar{\psi}^{\dot\alpha}$. We have Pauli matrices ...
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32 views

Diiference between three squashed sphere and three sphere and number of susy

First I know that three sphere $S^3$ and squashed sphere $S_b^3$ \begin{align} S_{b}^{3} = \begin{array} & R^2 \times S_{r}, \quad r=b, \quad b\rightarrow 0 \\ R^2 \times S_{r}, \quad ...
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146 views

Can pure-bosonic string theories exist in curved spacetime?

Question: Can there be a consistent non-supersymmetric pure-bosonic string theory in some curved spacetimes? Reason: Since fields with certain amount of negative mass can exist in curved spacetime ...
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45 views

Hypermultiplet as BPS particles

In the third paragraph of page 7 of the paper arxiv:1112.3984 it mentions that we form a basis out of hypermultiplets on the charge lattice $\Gamma$. My questions are: In what sense do we form such ...
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Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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54 views

Concerning topology of BPS states of the M5-brane

My question is about the M5-brane in M-theory. I would like to know whether the BPS states of the M5-brane worldvolume theory (especially the 1/2 BPS and 1/4 BPS ones) are independent of the topology ...
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2answers
454 views

Alejandro Rivero's correspondence: diquarks and mesons as superpartners of quarks and leptons

The idea of “hadronic supersymmetry” originated in the mid-1960s and derives from the observation that baryons and mesons have similar Regge slopes, as if antiquarks and diquarks are superpartners. ...
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2answers
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How can the mass of Higgs give preference to SUSY vs multiverse?

According to the documentary Particle Fever, the precise value of the Higgs boson's mass could give more credence to either SUSY or multiverse theories. If the mass had been 115 GeV or below SUSY ...
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3answers
388 views

Problems book recommendation on supersymmetry, supergravity and superstring theory

I'm learning supersymmetry, supergravity and superstring. I want some problems books to have some idea in this area. Is there this kind of books? Or are there some papers that have many solved model?
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33 views

Can we have supersymmetry using real scalar instead of complex scalars?

I am aware that a suersymmetric theories containing a complex scalar a Weyl fermion and an auxiliary field exist. I was wondering if we can have something analogous using real and not complex scalar ...
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1answer
462 views

Instantons in Witten's supersymmetry and Morse theory

I'm reading Witten's paper on supersymmetry and Morse theory and am confused about the details of the instanton calculation which he uses to define a Morse complex (beginning at page 11 of the pdf) . ...
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1answer
81 views

Calabi Yau Motivation

I have just begin to study Calabi Yau compactification. Looking in many book I found that, if we start with a critical superstring theory in $D=10$, we are in search of a compact $D=6$ Calabi Yau ...
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16k views

Supersymmetry vs multiverse

I'm a complete noobe in physics and quite honestly need help. My question is simple, based on CERN's tentative findings stating the Higgs boson at a mass of ~125 GeV: Is the physics community leaning ...
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70 views

Anomaly polynomial of Hitchin system $\mathcal{N}=2$ 4d SQFT

I would like to ask about mathematical background of this object. So, I am trying to puzzle out with 4d $\mathcal{N}=2$ SQFT. As far as I can gather this theory can be described in terms of ...
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1answer
96 views

Canonical spinors from gauge transformations

In this 2006 paper, http://arxiv.org/abs/hep-th/0610128, there is the concept of gauge transformation and how was it employed that I do not fully understand. Note, what will be talked about below is ...
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1answer
140 views

Where does the “Supersymmetry” in Witten's proof of the Morse inequalities come from?

Where does the "Supersymmetry" in Witten's proof of the Morse inequalities (original paper and outline of proof for mathematicians) come from? Hopefully someone can provide an intuitive understanding? ...
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53 views

Representation theory and the Nekrasov partition function

Is there any review or lecture notes on the Nekrasov partition function which particularly thinks of this from a representation theorist's point of view? Some possibly related references I know of ...
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1answer
71 views

Dimensional reduction of SUSY theories

I know that if one reduces 10 dimensional $\mathcal{N}=1$ SYM theory to 4 dimensions one gets $\mathcal{N}=4$ SYM. There are other examples also. I have two related questions regarding this fact. ...
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72 views

Supersymmetric transformation of general Wess-Zumino Lagrangian

I suspect that I might have understood something wrong here. I'm trying to show that the general Wess-Zumino Lagrangian \begin{align} \mathcal{L} &= \int d^2\theta d^2\bar{\theta} K(\Phi^*, \Phi) ...
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42 views

Can i use the $y^*$ representation of the chiral covariant derivatives on a superfield that contains both $y$ and $y^*$?

Imagine I want to compute this $$D^{\dagger2}D_{\alpha}(\Phi^*\Phi)$$ where the $D$-s are super-covariant derivatives and $\Phi$ is a chiral superfield. Following the notation of this review on ...
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0answers
24 views

Which is the analogous of the unitarity constraint of chiral perturbation theory in superchiral perturbation theory?

I am trying to reconstruct something and I would appreciate omeone helping me filling the gaps. To motivate my question let's first consider chiral perturbation theory with up and down quarks. This is ...
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0answers
52 views
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0answers
216 views

Book with solved examples and exercise problems for SUSY

I am learning supersymmetry right now. I am mostly following Bailin and Love. I try to connect all the steps from the book and complete the derivations in order to get comfortable with the ...
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1answer
80 views

Why must superpartners have the same gauge quantum numbers?

The title leaves it quite clear, why must superpartners have the same gauge quantum numbers?