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{{Quantum field theory}}
'''Center vortices''' are line-like [[topological defect]]s that exist in the [[vacuum state|vacuum]] of [[Yang–Mills theory]] and [[Quantum chromodynamics|QCD]]. They seem to play an important role in the [[color confinement|confinement]] of [[quark]]s.


==In SU(''N'') theories==
Center vortices are line-like topological defect that carry a gauge charge equal to one of the [[center (group theory)|center]] elements of the gauge group. In the case of SU(''N'') gauge theories, these are the constant matrices:
:<math>z_n = e^{\frac{2\pi in}N} I\;,</math>
where ''I'' is the unit matrix. These elements form the abelian subgroup [[modular arithmetic|'''Z'''<sub>''N''</sub>]]. Under such center elements, quarks transform as
:<math>\psi \to e^{\frac{2\pi in}N}\psi\;,</math>
while [[gluon]]s are invariant. This means that, if quarks are free (like in the [[Deconfinement|deconfined phase]]), the center symmetry will be broken. Restoration of the center symmetry will imply confinement. [[Gerard 't Hooft|'t&nbsp;Hooft]] first put this on a more rigorous footing.<ref>{{cite journal|author=G. 't Hooft|authorlink=Gerard 't Hooft|title=On the phase transition towards permanent quark confinement|journal=Nucl. Phys.|volume=B138|year=1978|pages=1|doi=10.1016/0550-3213(78)90153-0|bibcode = 1978NuPhB.138....1T }}</ref>


The two phases in the theory can be distinguished based on the behavior of the vortices.<ref name="Engelhardt">{{cite journal|author=M. Engelhardt|author2=K. Langfeld|author3=H. Reinhardt|author4=O. Tennert|title=Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition|journal=Phys. Rev.|volume=D61|pages=054504|year=2000|doi=10.1103/PhysRevD.61.054504|arxiv = hep-lat/9904004 |bibcode = 2000PhRvD..61e4504E }}</ref> When considering a certain [[Wilson loop]], if the vortices are generally long, most vortices will only pierce the surface within the Wilson loop once. Furthermore the number of vortices piercing this surface will grow in proportion to the area of the surface. Due to the vortices suppressing the value of the [[vacuum expectation value]] of the Wilson loop, this will lead to an area-law, i.e. the Wilson loop ''W''(''C'') behaves like
Opulence. Maybe there's something in the air of Paris that inspires it.<br><br>There's the proliferation of palais (petit or grand) for designers to show their collections in, the galleries filled with florid, lurid art, and the haute couture, of course, opulence cubed and then wrapped in duchesse satin for good measure. They all do something to designers, no matter how minimally minded.<br><br>It's certainly done something to Marc Jacobs. Compare and contrast the first Louis Vuitton collection he presented oh-so-quietly 16 years ago with the ball-busting extravaganza unveiled last Wednesday, part �Turn Back Time� video, part Paul Verhoeven's Showgirls<br><br>
:<math>\langle W(C)\rangle \propto e^{-\sigma A}\;,</math>
It was an indulgent farewell to a house that has helped redefine the meaning of luxury goods in the 21st century. Indulgent for Jacobs, but also for the audience, a funereal feast for the eyes, Jacobs' all-black swansong. The Stephen Jones headdresses were inspired by Ziegfeld Follies and Cher's 1986 Oscars outfit<br>
where ''A'' is the area spanned by the loop. The constant &sigma; is called the string tension. This behavior is typical of confinement. However, when considering a regime where vortices are generally short &mdash; i.e. they form small loops &mdash; they will usually pierce the surface of the Wislon loop twice in opposite directions, thus leading to the two contributions canceling. Only vortex loops near the Wilson loop itself will pierce it once, thus leading to a contribution scaling like the perimeter:
Says it all<br>
:<math>\langle W(C)\rangle \propto e^{-\alpha L}\;,</math>
Jacobs declared that the collection was obsessed with �pure adornment�, reasoning that �connecting with something on a superficial level is as honest as connecting with it on an intellectual level�. That's an interesting conceit. Contemporary fashion, like contemporary art, tends to be overthoug<br><br>
with ''L'' the length of the Wilson loop, and &alpha; some constant. This behavior signals there is ''no'' confinement.


In [[Lattice gauge theory|lattice simulations]] this behavior is indeed seen.<ref name="Engelhardt"/> At low temperatures (where there is confinement) vortices form large, complex clusters and percolate through space. At higher temperatures (above the deconfinement phase transition) vortices form small loops. Furthermore it has been seen that the string tension almost drops to zero when center vortices are removed from the simulation.<ref name="Faber">{{cite journal|author=M. Faber|author2=J. Greensite|author3=&Scaron;. Olejník|title=Direct laplacian center gauge|journal=JHEP|volume=11|pages=053|year=2001|doi=10.1088/1126-6708/2001/11/053|arxiv = hep-lat/0106017 |bibcode = 2001JHEP...11..053F }}</ref> At the other hand, the string tension remains approximately unchanged when removing everything ''except'' for the center vortices. This clearly shows the close relation between center vortices and confinement. Aside from this it has also been shown in simulations that the vortices have a finite density in the continuum limit (meaning they are not a lattice artifact, but they do exist in reality), and that they are also linked with chiral symmetry breaking and topological charge.<ref name="Faber"/>
If not by designers, then certainly by critics. After all, we have to justify our presence there. And the Air Miles we rack <br>.
Marco Zanini also showed his final collection for the house of Rochas. He's moving to Schiaparelli. Like Jacobs, he was obsessed with surface, with dumb, straightforward beauty. His was sugary sweet, in pastels that made your teeth ache, dedicated to Tennessee Williams' The Glass Menager<br>.
Banish thoughts of tormented southern belles. Zanini focused on the crystalline beauty of said ornaments, bonding devor� velvet to organza and freckling iridescent fabrics with Swarovski g<br><br>


One subtlety concerns the string tension at intermediate range and in the [[1/N expansion|large-''N'' limit]]. According to the center vortex picture, the string tension should depend on the way the matter fields transform under the center, i.e. their so-called ''N''-ality. This seems to be correct for the large-distance string tension, but at smaller distances the string tension is instead proportional to the quadratic [[Casimir invariant|Casimir]] of the representation &mdash; so-called Casimir scaling. This has been explained by domain formation around center vortices.<ref name="domains">{{cite journal|author=J. Greensite|author2=K. Langfeld|author3=&Scaron;. Olejník|author4=H. Reinhardt|author5=T. Tok|title=Color screening, Casimir scaling, and domain structure in G(2) and SU(N) gauge theories|journal=Phys. Rev.|volume=D75|pages=034501|year=2007|doi=10.1103/PhysRevD.75.034501|arxiv = hep-lat/0609050 |bibcode = 2007PhRvD..75c4501G }}</ref> In the large-''N'' limit, this Casimir scaling goes all the way to large distances.<ref name="Greensite">{{cite journal|author=J. Greensite|title=The confinement problem in lattice gauge theory|journal=Prog. Part. Nucl. Phys.|volume=51|year=2003|pages=1|doi=10.1016/S0146-6410(03)90012-3|arxiv = hep-lat/0301023 |bibcode = 2003PrPNP..51....1G }}</ref>
Maria Grazia Chiuri and Pier Paolo Piccioli took a precious approach, too. Their Valentino collection was inspired by the Rome Opera, apparently. In actual fact, it was all about the heavily embellished surfaces of lace and tulle. Lawn shirts seemed [http://data.Gov.uk/data/search?q=included included] purely as foil for all that decoration, a palette clean<br><br>


==In gauge theories with trivial center==
It would have made it easier to enjoy Hedi Slimane's latest Saint Laurent collection if you could take it at face value. Look! Sequinned lips! Flames! Lurex pop-socks! Removed from the heritage of Saint Laurent, it had a pop, pap appeal. If you stopped looking for a hidden depth, the soul-searching that Yves Saint Laurent made an intrinsic part of his fashion, Slimane ticked bo<br><br>
A gauge group like SO(3) has a trivial center, but SO(3) gauge theory is expected to be identical to SU(2) gauge theory. This discrepancy is due to the fact that, rather than the center, it is really the [[homotopy group]] &pi;<sub>1</sub> which should be considered.<ref name="Greensite"/> Also mark that a theory like [[G2 (mathematics)|'''G'''<sub>2</sub>]] gauge theory does not have a long-range string tension, which is consistent with the center vortex picture. In this theory, gluons can screen quarks, leading to color singlet states with the quantum number of quarks. Casimir scaling is, however, still present at intermediate ranges, i.e. before string breaking occurs. This can be explained by domain formation.<ref name="domains"/>


==See also==
Girls who want to look like that will love to dress in t<br>s.
* [[QCD vacuum]]
Karl Lagerfeld has always been about surface. His toying with the hallmarks of Chanel - tweeds, camellias, pearls, chains, those two-tone shoes - has always been about ironic appropriation, post-modern reinterpretation. It's the fashion equivalent of Jeff Ko<br><br>


==References==
He showed his latest Chanel collection in an art gallery. At least, it was on the surface. It was all fake, only the clothes were real. And they were pure Chanel, the art-house backdrop just that. I kept thinking of something Dinos Chapman once said to me: �I think that the art world and the high-end fashion world� are the same peop<br>.�
{{reflist|2}}


[[Category:Gauge theories]]
People wanted to buy the Chanel works of art as surely as they wanted to buy the Chanel clothes. They both became post-modern commod<br>ies.
[[Category:Quantum chromodynamics]]
That's looking below the surface, though, behind the opulence of Chanel's specially woven, artfully unravelling tweeds that resembled rag-rugs, the canvas [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine Bags Outlet] with a 2.55 fa�ade painted on the front, the graffitied art-student backpacks. They were just great, covetable fashion, brilliant pro<br><br>s.
 
That brings us, inevitably, to Phoebe Philo. She's known for great products - photography is banned in the C�line showroom for fear of rampant copying. And rightfully so. Still, that oft-imitated C�line hallmark is an ascetic aesthetic. Philo is the last designer one imagines inclined to opu<br><br>e.
 
But her riotously messy spring C�line collection felt fresh and energetic, pleated skirts bouncing below an elongated torso, fringe swaying on latticed leather bags, mashed-up metal formed into enamelled bracelets and <br>els.
Couture, of course, breeds opulence. Riccardo Tisci halted his made-to-measure line this year, but the handicraft of couture infected his spring collection, from the crystal-encrusted masks, to feather-embroidered bodices, to a series of sequinned, sinuous multi-pleat evening <br><br>s.
 
Those were old-school opulent. For modern couture, and a contemporary opulence, fashion turns to Raf Simons. His last Dior haute-couture collection met mixed reviews, but has inspired many a designer. The throbbing mood of Africa that beat through the collections, albeit slightly hackneyed, can be traced to S<br>ons.
This time, he pushed his aesthetic further still. It felt a collection in flux, sitting halfway between Dior past and Simons future, a cross-pollination. The inspiration was flowers, a theme at the very root of Dior. But the best [https://Www.google.com/search?hl=en&gl=us&tbm=nws&q=summary&btnI=lucky summary] was the least ostentatious: Simons' shirtdresses, twisted takes on the white cotton coats of workers corkscrewing around the body in a fascinating surface of complex <br><br>s.
 
So, French fashion is all about surface. Where does that leave Rei Kawakubo and Junya Watanabe, or Hussein Chalayan? The visual is just a fragment of what they offer, thinking clothes for the thinking woman. Jacobs may be in love with �beauty for beauty's sake�, but this trio of talents begs for somethin<br>more.
They all had a stellar, cerebral season: Watanabe creating an idiosyncratic ode to the spaghetti Western, Chalayan a paean to the windswept beach, while Kawakubo presented 23 non-outfits that challenged our perceptions of what fashion actually represents. She stated that she had no new ideas, so didn't create c<br><br>es.
 
If only other designers could follow her lead and thin out th<br>herd.
The surface of this deep-thinking threesome's clothing was universally impressive, but it's what lies beneath that really interests. Opulent intelligence? Their clothes beg dissection and discussion. To intellectualise a fashion show isn't automatically to over- intellectual<br><br>it.
 
Ultimately, that's what fashion is about. Surface is all well and good. But you have to get someone inside the damn clothes for it to all make<br><br>se.
 
It's ideological, as well as physical. At least, it is when it's really great.

Latest revision as of 16:25, 11 August 2014


Opulence. Maybe there's something in the air of Paris that inspires it.

There's the proliferation of palais (petit or grand) for designers to show their collections in, the galleries filled with florid, lurid art, and the haute couture, of course, opulence cubed and then wrapped in duchesse satin for good measure. They all do something to designers, no matter how minimally minded.

It's certainly done something to Marc Jacobs. Compare and contrast the first Louis Vuitton collection he presented oh-so-quietly 16 years ago with the ball-busting extravaganza unveiled last Wednesday, part �Turn Back Time� video, part Paul Verhoeven's Showgirls

It was an indulgent farewell to a house that has helped redefine the meaning of luxury goods in the 21st century. Indulgent for Jacobs, but also for the audience, a funereal feast for the eyes, Jacobs' all-black swansong. The Stephen Jones headdresses were inspired by Ziegfeld Follies and Cher's 1986 Oscars outfit
Says it all
Jacobs declared that the collection was obsessed with �pure adornment�, reasoning that �connecting with something on a superficial level is as honest as connecting with it on an intellectual level�. That's an interesting conceit. Contemporary fashion, like contemporary art, tends to be overthoug

If not by designers, then certainly by critics. After all, we have to justify our presence there. And the Air Miles we rack
. Marco Zanini also showed his final collection for the house of Rochas. He's moving to Schiaparelli. Like Jacobs, he was obsessed with surface, with dumb, straightforward beauty. His was sugary sweet, in pastels that made your teeth ache, dedicated to Tennessee Williams' The Glass Menager
. Banish thoughts of tormented southern belles. Zanini focused on the crystalline beauty of said ornaments, bonding devor� velvet to organza and freckling iridescent fabrics with Swarovski g

Maria Grazia Chiuri and Pier Paolo Piccioli took a precious approach, too. Their Valentino collection was inspired by the Rome Opera, apparently. In actual fact, it was all about the heavily embellished surfaces of lace and tulle. Lawn shirts seemed included purely as foil for all that decoration, a palette clean

It would have made it easier to enjoy Hedi Slimane's latest Saint Laurent collection if you could take it at face value. Look! Sequinned lips! Flames! Lurex pop-socks! Removed from the heritage of Saint Laurent, it had a pop, pap appeal. If you stopped looking for a hidden depth, the soul-searching that Yves Saint Laurent made an intrinsic part of his fashion, Slimane ticked bo

Girls who want to look like that will love to dress in t
s. Karl Lagerfeld has always been about surface. His toying with the hallmarks of Chanel - tweeds, camellias, pearls, chains, those two-tone shoes - has always been about ironic appropriation, post-modern reinterpretation. It's the fashion equivalent of Jeff Ko

He showed his latest Chanel collection in an art gallery. At least, it was on the surface. It was all fake, only the clothes were real. And they were pure Chanel, the art-house backdrop just that. I kept thinking of something Dinos Chapman once said to me: �I think that the art world and the high-end fashion world� are the same peop
.�

People wanted to buy the Chanel works of art as surely as they wanted to buy the Chanel clothes. They both became post-modern commod
ies. That's looking below the surface, though, behind the opulence of Chanel's specially woven, artfully unravelling tweeds that resembled rag-rugs, the canvas Celine Bags Outlet with a 2.55 fa�ade painted on the front, the graffitied art-student backpacks. They were just great, covetable fashion, brilliant pro

s.

That brings us, inevitably, to Phoebe Philo. She's known for great products - photography is banned in the C�line showroom for fear of rampant copying. And rightfully so. Still, that oft-imitated C�line hallmark is an ascetic aesthetic. Philo is the last designer one imagines inclined to opu

e.

But her riotously messy spring C�line collection felt fresh and energetic, pleated skirts bouncing below an elongated torso, fringe swaying on latticed leather bags, mashed-up metal formed into enamelled bracelets and
els. Couture, of course, breeds opulence. Riccardo Tisci halted his made-to-measure line this year, but the handicraft of couture infected his spring collection, from the crystal-encrusted masks, to feather-embroidered bodices, to a series of sequinned, sinuous multi-pleat evening

s.

Those were old-school opulent. For modern couture, and a contemporary opulence, fashion turns to Raf Simons. His last Dior haute-couture collection met mixed reviews, but has inspired many a designer. The throbbing mood of Africa that beat through the collections, albeit slightly hackneyed, can be traced to S
ons. This time, he pushed his aesthetic further still. It felt a collection in flux, sitting halfway between Dior past and Simons future, a cross-pollination. The inspiration was flowers, a theme at the very root of Dior. But the best summary was the least ostentatious: Simons' shirtdresses, twisted takes on the white cotton coats of workers corkscrewing around the body in a fascinating surface of complex

s.

So, French fashion is all about surface. Where does that leave Rei Kawakubo and Junya Watanabe, or Hussein Chalayan? The visual is just a fragment of what they offer, thinking clothes for the thinking woman. Jacobs may be in love with �beauty for beauty's sake�, but this trio of talents begs for somethin
more. They all had a stellar, cerebral season: Watanabe creating an idiosyncratic ode to the spaghetti Western, Chalayan a paean to the windswept beach, while Kawakubo presented 23 non-outfits that challenged our perceptions of what fashion actually represents. She stated that she had no new ideas, so didn't create c

es.

If only other designers could follow her lead and thin out th
herd. The surface of this deep-thinking threesome's clothing was universally impressive, but it's what lies beneath that really interests. Opulent intelligence? Their clothes beg dissection and discussion. To intellectualise a fashion show isn't automatically to over- intellectual

it.

Ultimately, that's what fashion is about. Surface is all well and good. But you have to get someone inside the damn clothes for it to all make

se.

It's ideological, as well as physical. At least, it is when it's really great.