New numerical results and novel effective string predictions for Wilson loops

JHEP04(2013)097

Received: April 4, 2013 Accepted: April 4, 2013 Published: April 16, 2013

Erratum: new numerical results and novel effective

string predictions for Wilson loops

M. Bill´o, M. Caselle and R. Pellegrini

Dipartimento di Fisica Teorica, Universit`a di Torino,

and Istituto Nazionale di Fisica Nucleare – sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy

E-mail: billo@to.infn.it,caselle@to.infn.it,pellegri@to.infn.it

Erratum to: _{JHEP01(2012)104}

Abstract: _{We correct a few misprints present in the published version, regarding eq.s} (4.30), (4.35), (A.4) and (A.6). Plots and results of the paper are not affected since they were derived from the correct formulae.

c

JHEP04(2013)097

The published version of this paper unfortunately contains some misprints in four displayed equations, of which we list below the correct form. We remark that plots and overall results of the paper are not affected by these misprints since they were derived from the correct formulae.

Eq. (4.30) must be replaced by the following one: W(A, u) =√2πσ|N |2 2 u α 4 r π 2σ_Ae −σAX k cke−2πuˆ k × ( 1 + 1 σ_A  α2 − 4 32 + α_{− 2} 2 πuˆk + 2π 2 u2ˆk2  + 1 (σA)2  α4 − 40α2 + 144 2048 + α3 − 6α2 − 4α + 24 64 πuˆk + 3 16(α 2 − 8α + 12)π2u2ˆk2+ (α_{− 6)π}3u3ˆk3 + 2π4u4kˆ4  + O  1 (σA)3 ) (4.30) Eq. (4.35) must be replaced with

ˆ L3(u) =

π 24

4

6(D + 24)Du4E42(iu)− 3D(D − 8)(D − 12)u 2

E4(iu)E2(iu)E2(i/u) +D(D− 4)(D − 8)(D − 12) 8 E 2 2(iu)E 2 2(i/u)  −π 24 3 4D(D_{− 12)u}3E6(iu)  1₋π 3uE2(iu)  +π 24 2 3 64D(D− 4)(D − 12)u 2 E4(iu) −(D + 4)D(D−4)(D−12) 256 E2(iu)E2(i/u)  +(D + 12)(D + 4)(D− 4)(D − 12) 32768 . (4.35) Eq. (A.4) becomes

E2k(τ ) = 1 + 2 ζ(1_{− 2k)} ∞ X n=1 σ2k−1(n) q n , (A.4)

Finally, eq. (A.6) should become

E2(τ ) = 1− 24 ∞ X n=1 σ1(n) q n , E4(τ ) = 1 + 240 ∞ X n=1 σ3(n) q n , E6(τ ) = 1− 504 ∞ X n=1 σ5(n) q n . (A.6) Acknowledgments

We thank M. Bruno for pointing to us a few of the above misprints.