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

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Higgs mechanism preserving supersymmetry

It is said that if supersymmetry was unbroken, masses of the superpartners would be equal. But at least for MSSM there are no SUSY-invariant terms that would allow the electroweak SSB, as far as I ...
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31 views

General framework of Supersymmetry [on hold]

Even the people who are skeptical about SUSY are happy with the SUSY searches going on at LHC because they recognize that SUSY's general framework is quite flexible and the search strategy used in ...
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Question about the superconformal index

According to arXiv:1507.08553v1, the superconformal index, defined by $$I(\beta_j) = \mbox{Tr}_{\mathcal{H}}(-1)^F e^{-\gamma\{Q,Q^\dagger\}}e^{-\sum_{j}\beta_j t_j}$$ is independent of the ...
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1answer
27 views

Question about the expression of Witten Index

I am studying supersymmetry by myself. I do not understand the expression of Witten index, which is ${\rm Tr}(-1)^{F}$. What does it mean by writing $-1$ to the power of an operator $F$? Is this ...
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70 views

Susy transformation for gauge multiplet

How can the supersymmetrie transformation $\delta A_\mu = \frac{1}{2} \overline{\epsilon}\gamma_\mu \psi $ be derived from the susy algebra ( or group ). Where $ (A_\mu , \psi)$ are in a gauge ...
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43 views

What are anticommuting spinor parameters $\zeta^\alpha$?

I'm reading Martin F.Sohnius, Introducing supersymmetry, page 82. It is the first time he introduces the anticommuting spinor parameters $\zeta^\alpha$ to calculate the supersymmetry variations of a ...
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54 views

Problems with covariant action of the superstring

I was reading Kiritsis notes (http://arxiv.org/abs/hep-th/9709062), at page 105/106 (equation 10.1), where he has a covariant action of the superstring including the gravitino. I have problems showing ...
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51 views

Why torsion vanishes in supergravity?

Why is it (more often than not) considered in supergravity that the torsion vanishes in Cartan's first structure equation? What does the vanishing of the torsion imply?
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68 views

Semi-infinite forms?

I am reading Vafa's paper 'Topological Mirros and Quantum Strings'. In this paper, the author says the Hilbert Space of a fermionic string theory corresponds to the space of semi-infinite forms on the ...
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1answer
48 views

contraction of the spinor F with a conjugate spino $\bar{\epsilon}$ is bosonic?

In this Why $\delta F = B\epsilon$ and not $F=B \epsilon$ in supersymmetry?, I asked ACuriousMind why would one epsilon be without a bar and the other with a bar here: $$\delta F = B\epsilon, \tag{1} ...
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How does one determine the genus of the ultraviolet curve from Seiberg-Witten curve?

In Gaiotto's construction of 4d ${\cal N}=2$ theories, one starts with 6d (2,0) theory and compactify it on the Riemann surface, which is called the ultraviolet curve of the ${\cal N}=2$ theory. In ...
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66 views

Fayet-Iliopoulos terms

It is mentioned in first page of this paper by Seiberg and Komargodski that the Lagrangian in superspace of a $U(1)$ gauge SUSY theory with FI terms is not gauge invariant. However, the FI terms in ...
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Supersymmetric variation of $F$ term using super Jacobi identity [closed]

Basically, i am solving problems in note with a slightly different notation. \begin{align} [Q_\alpha F] = -i \lambda_\alpha (x), \quad [ \bar{Q}_{\dot{\alpha}},F] = -i \bar{\chi}_{\dot{\alpha}} ...
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1answer
33 views

To which type of particles gauginos are supposed to couple?

I wonder about to which type of particles gauginos couple in general. I admit my knowledge in supersymmetry is very limited. Let's take an example: The photino. If it behaved similar to the photon, it ...
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66 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
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93 views

Supercovariant Derivative action

My query is with Weinberg Vol3 equation just above 26.7.22 Weinberg follows Majorana Superfield formalism. Where, covariant derivative is defined as, $$D_{R\alpha}=-\epsilon_{\alpha ...
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1answer
51 views

Decomposing massless N=8 SUGRA multiplet into multiplets of massless N=4

The only massless $N=8$ SUGRA multiplet is given by $(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$ where the greek upper ...
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46 views

Lorentz group in SUSY

Why do we carry Lorentz group to be included also in supersymmetry? That is after we extend our symmetry to supersymmetry, we carry with us the Lorentz group. Why not other group instead?
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Baryonic operators in ${\cal N}=1$ $U(N)$ SQCD in four dimensions

Seiberg's duality is usually considered as a duality for $SU(N_c)$ theories with $N_f$ flavors. In his case, the vacuum for $N_f \geq N_c$ is parameterized by mesons $M$ and baryons ${\bar B}$ and ...
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1answer
35 views

Why are only certain fluxes allowed in 11D SUGRA?

In Type IIA/IIB string theory we can have various fluxes, such as the 3-form H-flux, and the various Ramond-Ramond fluxes in even/odd dimensions. In 11D SUGRA, however, the field content seems to ...
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1answer
80 views

Geometry of spacetime and spinor bilinears

In this paper (http://arxiv.org/abs/0704.0247) p.20, the author says in the section titled Geometry of spacetime the following: In order to obtain the spacetime geometry, we consider the spinor ...
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75 views

Killing vector and one-form [closed]

p. 21 in this paper (http://arxiv.org/abs/0704.0247) $V$ is Killing vector, where $V^2 = −4b\bar{b}$, which means it is timelike Killing vector. The authors say: From $V^2 = −4|b|^2$ and $V = ...
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1answer
56 views

How do we know if a Killing Spinor is Time-like or Null?

How to know whether a Killing spinor orbit is time-like or null? This is present in a paper like this 29/39 here. I'm not asking for a technical answer, just a logical cliche answer chit-chat answer. ...
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25 views

Basic Dirac Spinors question

Here p. 25, it says Generically, the space of Dirac spinors has $2^{d/2}$ (complex) components, and one can recast them in terms of the complexified space of forms on $\mathbb{R}^{d/2}$. My ...
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69 views

What does $δF=0$ imply?

Please have a look here section 12.6. It says here that Given the action of a supergravity theory, it is generally useful to search for solutions of the classical equations of motion. It is ...
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2answers
121 views

Why $\delta F = B\epsilon$ and not $F=B \epsilon$ in supersymmetry?

We can express supersymmetric transformations as $$\delta F = B\epsilon, \tag{1} $$ $$\delta B = F\bar{\epsilon},\tag{2}$$ where $B$ and $F$ denote the bosons and fermions, respectively, in the theory ...
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1answer
93 views

What are susy transformations for N=2 sugra?

Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories. As suggested by some books and papers on ...
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122 views

I do not understand this comparison?

It is frequently discussed that to find solutions having some sort of supersymmetry is easier than solving Einstein’s equations of motion. I do not understand this discussion though. Specifically, ...
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139 views

Why supergravity is extension of GR?

Why is it that supergravity is an extension to general relativity? In what ways? What I have read until now says the following: GR got itself concerned with gravity after the revolution of special ...
2
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1answer
58 views

Superpotential for Gaussian potential well? [closed]

so I am looking for the super potential of a Gaussian well, namely $V= -e^{-x^2/2}$, and the super potential has to satisfy the Riccati equation,$ − W′ ( x ) + W ( x ) = V ( x ) − a$. Somehow I ...
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Which are some best books to learn supersymmetry?

I am interested in a book that is mathematically precise. I am not expecting a mathematicians book like the one by Deligne.
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278 views

Apparent failure of SUSY nonrenormalization theorem

I am having trouble reconciling two pieces of information. Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, $h$ and $\hat{h}$. ...
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1answer
43 views

Electro-mangetic duality, Quantum electro dynamics and N=4 SYM

This question is extension of Electro magnetic duality, Strong weak duality and N=4 super Yangmils which i asked before. Here what i want to know is compare of QED and N=4 SYM in terms of ...
2
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1answer
40 views

Nahm's theorem and related with SYM ;other theories

To study $S$-duality in more detail, i tried to read, Electric-magnetic duality and the Geometric Langlands Program. In section 2.1, there is a comment about 10d SYM. Excerpt from the paper above, ...
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Are SUSY transformations free from anomalies?

Although I've studied supersymmetic field theories for several years, there is a fundamental problem annoying me: Do SUSY transformations (including both the ordinary ones in various dimensions and ...
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2answers
46 views

How would superpartners explain dark matter? (Supersymmetry)

This is probably very basic but I can't quite find the answer in other questions. As I understand it we are hoping to create supersymmetric particles at the LHC (in this second run) and these ...
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1answer
54 views

Electro magnetic duality, Strong weak duality and N=4 super Yangmils

How we can interpret this self-dual, or duality in terms of generalized version of electro magneitc duality, or Strong weak duality. Let me address some basic information. First, electro magnetic ...
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67 views

Supersymmetry as a solution of hierarchy problem

Hierarchy problem is the statement of why the weak force is much stronger than gravity. In terms of coupling constant, weak force (Fermi coupling) is much larger than gravity (Newton's constant). I ...
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What is the Superpartner of a glass? [closed]

A little context: This summer I visited Switzerland and had the chance to tour CERN. While there, I saw through an open door this question written at the top of a chalkboard in someone's office. I ...
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1answer
55 views

Seiberg duality and IR fixed point

This question is related with Seiberg duality for $SU(N)$ gauge theory which states a duality between electric theory, $SU(N_c)$ gauge theory with $N_f$ flavors is dual to its magnetic theory, ...
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35 views

How can we use Majorana spinors for charged fermions in MSSM?

According to "Supersymmetry in Particle Physics" by Ian Aitchison (see e.g. p62 of arXiv), in the Minimal Supersymmetric Standard Model (MSSM) we can use Majorana language to build supermultiplets: ...
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210 views

Is a $SU(2)$ supergauge theory really a $SU(2)$ gauge theory?

Consider $SU(2)$ supergauge theory with $A$, a doublet of two chiral superfields in the fundamental representation. $$A= \begin{pmatrix} \Phi_1\\ \Phi_2 \end{pmatrix}$$ where $\Phi_1$ and $\Phi_2$ ...
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45 views

Superpotential Symmetry

Superpotential in general has the form $W=a_n\Phi^n$. If I require that my superpotential should be invariant under the following global transformation, $\delta \Phi=i\epsilon \Phi$ and $\delta ...
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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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Soft SUSY breaking fermion mass terms in MSSM for matter fields

In the Minimal Supersymmetric Standard Model, the chiral fermion fields (the Higgsinos) don't have any soft SUSY breaking mass terms and soft SUSY breaking trilinear interactions while their scalar ...
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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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State counting in the d = 1+2, $\cal{N} = 2$ vector multiplet

The question is from Box 8.2, page 282 of the book "Gauge Gravity Duality" by Ammon and Erdmenger. The link to the specific page from Google Books is here. According to the authors, a $\mathcal{N} = ...
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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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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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102 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 ...